Unless they are different on the RD boards grounding the tab doesn't actually test the transistor it just tests the coil, wiring, etc. I would venture a guess that the drive transistor or pre-driver is bad.

Shorted yes it would lock on a coil but a transistor can fail open as well.

I'm sorry but I'm not familiar with their boards and don't know what transistor types they use in the game but it should be a NPN and the tab should be the emitter. With that in mind and the game off if you put a meter in diode test, black lead on the tab and the red lead on each leg you should have a forward voltage drop of about .8-1.2V from the base to the emitter and a very high reading from collector to emitter (one leg will be a dead short to the tab as they are electrically connected). I'd suspect you won't see the base to emitter drop and it will be open indicating a bad transistor. Also If you have a logic probe you could probe the base of the transistor (just be careful and don't put the probe on the high-voltage legs of the transistor, could seriously damage it) while the game is in solenoid test mode and see if it cycles, if it does the pre-driver is working and the driver transistor is bad, if not the problem is the pre-driver or further up the logic chain of the board. You'd have to follow that back up the chain with the logic probe if that's the case.