Sounds like you hit the big ones. I didn't check the schematic to make sure you got the right transistor. If you are 100% sure the coil, diode, and polarity are good you might try getting a different driver board. Or testing from another game. If one of the driver chips are bad on the driver board and not the transistor it could be causing your issue. This would be extremely rare, but I guess could happen.
I assume you used an ohm meter on the transistor. To find the shorted one.