CE525 Captain and sole crewmember reports runway incursion at CHS during taxi in at night with rain. Aircraft is not equipped with windshield wipers.

Narrative

After completing an ILS to Runway 33 at CHS under night; IMC conditions with moderate to heavy rain with wind shear alerts; I was instructed to exit the runway at Taxiway E; and contact ground. After clearing the runway on Taxiway E (left); I contacted ground and was instructed left on Taxiway D; left on Taxiway F; cross Runway 3 (closed) and hold short of Runway 33. While taxiing along Taxiway F; I was searching for the hold short lines and was having a difficult time seeing due to the amount of rainfall on the windshield and reflection of the lights across the field as it gave everything a 'glassy' look. While taxiing forward; I made a comment (on ground) that maybe I could have back taxied and at that moment; I realized I had committed the nose of the aircraft onto the active runway. I quickly scanned right and I also noticed an aircraft just starting its takeoff roll and at that split moment; I elected to throttle up and accelerate to aggressively clear the runway. I advised Ground Control that I crossed which advised me that I was to hold at the runway. After shutdown; I immediately contacted the Tower and advised the Controller of my name and phone number. Obviously; my intention was not to create an unsafe situation for anyone. I felt that an immediate decision had to be made to stop or clear the runway and I elected to clear it; immediately. I felt that I was vigilant while operating and questioned ground on taxi instructions several times and was responded to accordingly and professionally. I am somewhat familiar with the airport. I believe the weather played a major role in inhibiting me for seeing the hold short markings. Moderate rain along with the lights in the background provided an environment that limited identification markings. Not having windshield wipers further inhibited my vision with the amount of rain.