You should go to
http://marvin3m.com/fix.htm. I don't know a better place for pinball repair.
Others may have some ideas, I'm still learning myself but here's how you can test to see if the coil is good (taken from that site)
Coil Test to Make sure Coil is Good.
Here's another method of testing coils, which is more "low-level". This will test if the coil itself is good, and that there is power at the coil.
Game is on and in "attract" mode, and the playfield lifted.
Connect an alligator clip to the metal side rail of the game.
Momentarily touch the other end of the alligator clip to the GROUND lead of the coil in question. This will be the coil lug with the single (thinner) wire attached. On coils with a diode, the ground coil lug is the one with the non-banded side of the diode connected. On FL11630 flipper coils F-14 Tomcat and later, touch the middle lug to ground.
The coil should fire (if you accidentally touch the alligator clip to the power side of the coil, the game will reset and/or blow a fuse, as you are shorting solenoid high voltage directly to ground).
If the coil does not fire, it may be a coil that is A/C relay selected. Push the center red coin door button down, and press the black button closest to the coin door. This will put the game in diagnostics mode. This should de-energize the solenoid A/C relay, and turn the power to the coil in question on.
If the coil still does not fire, either the coil itself is bad, or the coil's fuse is blown and power to the coil is not present.