It's not the coil.

Your solenoid driver board has problems that need to be addressed. You might want to just pick up the replacement board so you have a known good one to test with. The flippers shouldn't be active all the time, sounds like someone hacked the circuit to get the relay out of the picture.

Transistors can test good and still be bad.... most likely something in the chain is shorted on. It will cook the new coil and make it bad if the fuse on the rectifier assembly doesn't blow.

While you're at it, check your fuses for proper values. Despite seeing the game working when you picked it up, you should go through the checklists on pinwiki and probably here as well for "project game" - starting with testing everything on the rectifier board, then move to the solenoid driver board (which you know is already hacked up), then to the mpu and lamp boards.

For the future, you can measure a coil with an ohm meter to see if its good or not - anything under 1-2 ohms is shorted. Most likely the issue is a cooked transistor or predriver, but if the coil is now bad due to overfusing/locked on, it'll keep killing driver transistors if you don't fix everything in a systematic manner.