The pre-driver transistor is definitely the next thing to consider as the cause of the problem. The pre transistor chip is just a series of transistors in one package. It`s definitely possible for just one transistor within the IC to go bad. The next thing back from there is the 4 to 16 decoder, but the pre-driver transistor seems most likely.

Yes, the transistors in the IC can be tested the same way a dedicated transistor would be tested. Which pins each emitter, base, and collector are connected to in the IC is specified on the schematic.

I like to test the pre-driver transistors using a logic probe with the board in the game and the solenoid test running.