It is possible the previous owner left the transistor out because something in the circuit kept burning it up. No reason why you couldn't put it back in but if there was something wrong you would need to figure out exactly what is wrong. I think at very least I would take an ohms reading on the coil and make sure the coil isn't shorted. I am not sure what coil is in there but you could take a reading from another identical coil in the game and the reading should be the same. If after you replace the transistor and the coil get stuck on, turn the game off immediately. Whatever is driving the transistor is likely stuck on. You will need to back track from that transistor point and investigate.