BE20 Pilot reported what they thought was a dragging left brake. Instead of aborting; the pilot continued on to the destination where the aircraft became disabled on the runway after landing.

Narrative

I was on a contract trip in a BE20 I don't normally fly; but have flown it about X hours in the last 8 days and the airplane is about 80-90% common to the BE20 I routinely fly. The normal pilot is on vacation so I'm filling in and he relayed to me that another contract pilot reported difficulty getting the left parking brake to release in early month. I was cautious about using the parking brake for that reason; but after a few normal engage/disengage cycles felt it was operating normally; but still retained heightened awareness that it might be an issue on disengagement. The BE20 parking brake for this S/N operates simply; apply pedal pressure and pull the parking brake handle to engage and apply pedal pressure while reseating the handle to disengage.I was called yesterday about XA:15 and asked if I could go pick up the 2 passengers I had been flying over the last 8 days from ZZZ. I told the requester that I didn't have night landing currency per FAR 61.57(b)(1) so had to be shut down NLT 1 hour after sunset; which was XC:27; so NLT XD:27. Of course there were strong storms in the ZZZ terminal area and my departure was delayed slightly by ATC flow control; but I departed with enough time to comfortably be back prior to XD:27. The flight from ZZZ1-ZZZ was uneventful and I set the parking brake when I arrived at the FBO; the passengers were ready; and I was able to execute a quick turn after coordinating with the FBO for a total time from shutdown to taxi of about 13 minutes. The parking brake felt as if it released normally; but the airplane required slightly more left engine power than normal to make the required 135 degree right turn from parking to the taxiway. I attributed that to the fact that I hadn't let the airplane roll forward to build much momentum in order to not subsequently blow my exhaust on the line personnel. The taxi routing was all right hand turns out to the active runway and the winds were quite strong and gusty from the right rear quarter. I had to correct the airplane back to the right to regain center line a few times and I attributed that to the winds. I teach new King Air pilots that the brakes aren't needed much for taxi and that you can easily control taxi speed and lineup with Beta range and differential power. Even though I drifted left of center line a couple of times; given the winds; that did not feel abnormal.Of note; during my taxi I heard a regional carrier taxi from another FBO and query ground control if they would have a delay at the end of the runway prior to departure for their short repositioning flight to ZZZ2 because they were 'time sensitive.' Based on my 121 experience and general knowledge; I presumed they had diverted from ZZZ2 to ZZZ due to weather and were very close to timing out per FAR 117 rules and potentially impacting their presumed passengers. Ground told them they would have no delay and I knew they would be the next to depart after me. Tower kept me rolling with no need to stop at the end of the runway and I completed my normal Final Items flow; verbally confirmed they were complete; and began my normal takeoff roll. Initially I didn't note any undue directional control issues and used the accepted technique of advancing power at a slower-than-normal rate until the propellers were synchronized at their 2;000 RPM takeoff setting to avoid directional control issues; then advanced to takeoff power of about 1;950-2;000 ft/lbs of torque. All King Airs I have flown exhibit some directional control 'hunting' that can be attributed to slightly mismatched power settings exacerbated by normal crosswind challenges. Over time; I've learned where power levers need to be on the airplane I routinely fly to almost completely null out those challenges even in a strong crosswind takeoff (using slightly more power initially on the downwind engine for example). On this takeoff; I initially had slightly more challenges holding center line which I attributed to my relative lack offamiliarity with the particular airplane's power production coupled with strong; gusty left crosswinds. However; I realized that the airplane was drifting into the wind instead of away from the wind even though I had upwind aileron into the wind. That realization; and the thought that I must be dragging a left brake based on what the normal pilot had told me the week before both occurred as the airplane had drifted completely left of center line and was approaching the runway edge. This all occurred simultaneously with thoughts from my previous life as a military pilot where we had drilled into us to continue a takeoff with a suspected blown tire/directional control problem even below V1 after a certain speed since directional control problems increase with decreasing speed. Not wanting to go off the runway laterally at a high rate of speed and at V1 already; I rotated and the airplane leapt off the ground accompanied by an audible pop and a momentary activation of the stall warning horn. That is not normal.At 1G and zero knots; I now think I should have left the landing gear down but I instead performed my normal after takeoff flow of raising the gear. Once I was sure the airplane was accelerating and under control I radioed ZZZ Tower to tell them I was not going to continue my departure and that I may have blown a tire on their runway so they might want to perform an inspection. I also asked to remain in a wide pattern around the airport until I had further information. ZZZ Tower was excellent and provided great support; asking me to remain within 4 NM and that I was cleared to do as requested. I informed my passengers of our potential problem and that I would make a further decision once I heard back from the runway inspection. ZZZ Tower clearly was watching me through their binoculars because he told me that they were having problems seeing anything abnormal because I was at about 2;000 AGL. I descended to about 1;000 MSL for my next pattern while I heard the runway inspection in progress. I informed Tower of where I thought I had rotated based on a taxiway intersection; and that once the inspection was complete I would get out of the way so he could get the regional carrier going since I heard they were time limited. ZZZ Tower thanked me and told me they didn't see anything abnormal on my airplane (the gear was still retracted). The runway inspection didn't reveal any abnormalities either; so I elected to leave the airplane configured as it was and to proceed on my flight planned route. I gauged there wasn't any potential issues that would arise during the flight; but that I may have flat spotted and flattened a tire on the left-hand side which would be an issue on landing. In retrospect and after talking with a Mechanic at a very reputable national facility; I now think I 'could' have had an diagnosed and unmonitored brake fire since the BE20 doesn't have a system to monitor brake temperatures. I have never heard of that situation during my X years flying the airplane and going to annual recurrent training; and honestly didn't consider it until the next day. I still don't know if that was a potential issue.The flight to ZZZ1 was uneventful; but the sun had set and the Tower had closed at XD:00L. I cancelled my IFR flight plan at about 12 NM from the airport with it in sight and planned on a visual approach to Runway XX. There was a light GA airplane in the pattern for Runway XX doing multiple landings and my flow into the pattern put me landing just as he was turning from crosswind to downwind. Thinking I may still have a left main landing gear issue; I intentionally planned to land right of centerline and put it in my mind that I might have to use reverse thrust on only the right engine to help keep me on the runway if the airplane aggressively drifted left. The airplane has the aftermarket Raisbeck Epic Platinum package and I used their published approach speed for my calculated 11;000lb landing weight of 90 kts and touched down more firmly than normal right of centerline as planned about 500-1000 ft. down the runway. The airplane immediately felt as if the left main tires were flat and began a left drift. I did not use reverse and only put the power levers in Beta range and applied the wheel brakes. I had difficulty with directional control using differential braking and nose wheel steering and never did use differential power. The drift became more pronounced as the airplane slowed and I anticipated having to shut down the engines to avoid/minimize a prop strike. However; I was able to get the airplane stopped well short of a crossing runway (XY/YX) with no apparent damage from the cockpit. I radioed to the airplane in the pattern that I had just closed Runway XX due to an airplane issue and he changed his patterns to Runway XY. I took a second and told my passengers to hold on; gathered my wits; and performed a normal shutdown and securing of the airplane with the exception of leaving the beacon and strobes on since I was now stopped on an active runway at a now-uncontrolled airport since the landing was at XA:15L (12 minutes before my drop dead time). I then told my passengers to exit the airplane into the airport infield in case another airplane would try and land. I placed a phone call to ZZZ Approach after getting their clearance delivery number from ForeFlight to inform them of the problem at ZZZ1. A member of the 2 FBO's on the field (the one where the airplane is hangared) must have noticed the issue because he drove out to the airplane and was on the phone with the Airport Manager as he pulled up. I spoke with a Supervisor at ZZZ [Approach] via the phone and he said he'd shut down arrivals to runway XX/YY and would publish a NOTAM; but they had no way of informing VFR airplanes about the issue. I left the FBO person with the airplane and escorted my passengers with their bags to a closer FBO to transport them to their vehicle. I then got the number to a city fire station that has ARFF responsibility for the airport; called them; and asked them to bring a truck out with its lights flashing until the airplane could be moved off the runway. They arrived within 5 minutes and I now felt secure that a GA pilot wouldn't inadvertently land on the now closed runway and impact my airplane. The Airport Manager arrived shortly thereafter and turned off the lights to Runway XX/YY. [All traffic] continued to use Runway XY while we devised a plan to remove the airplane from Runway XX. Within about 20-30 minutes we had a crew of local mechanics; FBO; and military personnel coming up with a plan to recover the airplane so I departed the airport. In retrospect; without the strong winds I likely would have noticed a brake/directional control anomaly during taxi in ZZZ and likely would have returned to the FBO. Once airborne; I should have left the landing gear extended both for a visual inspection and to minimize any thermal damage. As I stated; the thermal issue didn't occur to me until the next day and my thoughts at the time were that I had already retracted the landing gear and that extending it wouldn't have given me any more information than I already had if the runway inspection didn't find rubber debris. Had the runway inspection found debris; my plan was to remain at ZZZ; devise a gameplan to include even going to ZZZ3 since they have a wide runway and a lot of ARFF like ZZZ; or land at ZZZ after getting a closer visual inspection of my landing gear. There was a lot of weather in the ZZZ terminal area to include storms with hail; lightning; and strong winds so the gameplan would have taken all of those weather factors into account. My only concern with the regional carrier was to minimize my impact on them once I knew the airplane wasn't in imminent danger and I didn't feel any pressure other than that; but it was another consideration that arose during the incident. Since the inspection didn't find debris; and not