Without seeing the machine - if the coil is firing in test mode I'd be testing if the ball registers the switch in test mode (not finger). As suggested earlier it maybe just bent / out of adjustment.
If you get stuck give us a yell.
+1 - I'd say the switch that the ball sits on has bent over the years just enough that the switch isn't being activated. Can't remember on Freddy for sure, but you should be able to access the switch under the playfield or if not, remove Freddy's head and you should be able to see what is going on. May even just be a loose wire on the switch itself. As you said, the coil is working, you just need to sort out the switch that activates the coil.
I am not sure if the Freddy playfield actually slides out or not, I have a feeling that it just lifts up. It may be something as simple as the ball launch plunger needs to be pulled back to allow the playfield to lift. Also make sure the lock down bar mechanism is actually unlocked.
