don't have the game but I would make sure there wasn't any other load on the circuit but the coil and if there is not I would probably check the (I call them anti-flyback diodes) across the coil is good and the right type. when the coil is de-energized you get a coil voltage spike in the opposite direction and if the diode is not there to give it a path to ground it can blow up the transistor

.4 to .6 is typical forward biased (positive to anode ....arrow part) and negative to line side.........and should be infinity reverse biased positive to line side and negative to arrow however you have to pull one side up (unsolder it) off the coil to get a good reading