Missing a ball should not be a problem... TAF should have 3 balls. Altough most games are designed pretty well so that balls should rarely get stuck, it is always possible. It can't be gone though, it should be somewhere, if not above the playing field then below it. Have you opened the machine?
The good thing about pinball games is that as long as the playing field itself is in good condition, anything can be fixed or replaced. If none of the solenoids fire up, it sounds like a blown fuse.
What I like about the later games, and only discovered after I owned my own TAF, is how clever the software and diagnostics are. If a switch on the playfield hasn't been hit in the last 50 games, it is considered broken. If it is stuck-on, it is considered broken too. Either way, the software is programmed to work around it, and still provide a playable game. If no switch is thrown during a game for x seconds, it assumes the ball is stuck somewhere, and fires all solenoids one by one, attempting to kick the ball somewhere. If a switch is flagged as broken, the display shows a small dot behind the credits counter ("Credits: 0." instead of "Credits: 0"), so operators can see at a glance if a machine needs service or not. Also, like many electrical devices in that era, they came with full electric diagrams. The electronic components are all before everything became SMD, so it's still possible to do basic circuit board repair yourself.
Yes, I love my machine, and am sad they have just about disappeared. Stern is afaik the only manufacturer left, but I'm not a huge fan of their games, altough Lord of the Rings was pretty cool. If you're interested, visit the Pinball Hall of Fame in Las Vegas, with over 150 working machines. Bring tons of quarters.