Do the rollover buttons score?

By "ball capture" I assume you mean the kickout holes?

Nearly everything you describe could be caused by a switch at score motor 1C being open. I say "nearly" though, because it should also prevent the pop bumpers from scoring.

But either the left and right kickout hole switches closing should activate the J relay, via a normally closed switch at motor 1C. Then when J energizes, the score motor should run, score motor switch 4C closes, and both kickouts should fire.

Other than the motor switches, the only other common thing I can think of in the path would be Jones plugs. The signal needs to get from the playfield to the bottom board and to the backbox. So if one is not plugged in, or not fully, maybe. Even though they look good, reseating them, and making sure they're in the correct spots might be worthwhile.