Did you replace the correct transistors for that solenoid as shown in the schematic for your game? If you replaced the driver and pre-diver transistors for the solenoid and it still locks on during start up, you need to look 'upstream' and test the buffer chip that controls the transistors (going by memory here). That could be checked by a logic probe. If you decide to just replace it without testing, it is a relatively cheap chip. But the damage may go even further upstream to the PIA chip, so again a logic probe would help. Circuit board soldering skills will most probably be needed.
I assume you checked for short circuits to wiring when looking over the solenoid and the boards.
This kind of repair has been covered many many times here, just search on "locked on solenoid" or similar to get the background. Pinwiki does not have anything yet on solenoids for Williams System 3-7, so Clay's guide would help (costs money).
Varistor is a two leg little lolipop shaped component in the silver power box in the cabinet where the service outlet is. It is probably not your problem unless the whole game is now dead.
Good luck, let us know how it goes and what the final answer was.
Don C.