M20G Pilot reported landing gear extension issues during final approach. After using the alternate extension procedure a landing was made during which the aircraft became uncontrollable and exited the runway.

Narrative

I was asked to do ferry flight on a M20G 'Mooney' from ZZZ1 to ZZZ in the afternoon.All was normal during the Initial Final Approach into Runway XX at ZZZ. It was not until 1 mile short Final when Tower Control Requested an immediate Left Turn to enter Left Downwind for Runway XX and then to be re-sequenced to be number 3 for Runway XX again. I was later told by a Control Tower Representative that there was training going on in the Tower and wanted to see a re-sequence of an approach.During the Go Around Procedure; Go-Around Thrust was set with Flaps to TO (takeoff) setting and GEAR Selection to UP upon Positive Rate.As I was turning Left Base for Runway XX; I went to position the Landing Gear to DOWN. But immediately noticed no Gear Motion was moving nor any indication that the GEAR was DOWN and LOCKED.It was at this point I requested a low approach for Visual Confirmation from the Tower. As I suspected; the Tower advised that the Landing Gear was NOT DOWN.I then requested an extended Downwind to begin reviewing the EMERGENCY GEAR EXTENSION PROCEDURE. I followed the Checklist but was unsuccessful in getting the Gear to Extend. While Turning the Manual Crank; the Handle would not Turn Clockwise as if something was Blocking the GEAR from Extending. There was no further guidance from the POH for this type of situation. After several attempts in trying to turn the handle; I finally elected to advise the Tower that I would attempt a GEAR UP LANDING.Tower requested that I attempt the GEAR UP LANDING on Runway XY in order to have their Main Runway available for incoming Traffic. I agreed and positioned the aircraft on a Left Downwind for Runway XY after the Go Around from Runway XX. During the Left Downwind; it came to my mind to see if the Gear would completely Retract Manually. I was in luck and the Gear did retract manually when turning the Crank Counterclockwise. With the Gear completely Retracted; I then attempted to see if it would now extend normally. After resetting the Landing Gear Circuit Breaker; I went to Position the Landing Gear handle Down and the indication NOW SHOWED DOWN and LOCKED.I request one more low approach to get visual confirmation on the GEAR from the Tower.Tower advised GEAR was DOWN! Tower then requested I enter a Right Downwind for Runway XX to be then cleared to Land on Runway XX.All event was then Normal up to the point when the NOSE WHEEL made contact with the Runway. For some reason I had a very STRONG PULL to the LEFT. I applied Full Right Rudder with Right Wheel Brake but was unsuccessful in the maintaining the Aircraft on the Runway.The aircraft came to a stop on the Left Side into the Dirt of Runway XX about 1/3 down.I called the FBO for a Tug; to position the aircraft over to [the FBO].There was no apparent damage to the Aircraft and I was uninjured during this incident.