Unlike most posts aboue flippers not working the issue with mine is that they are! The flippers work all the time, you don't need to coin the game or hit start or anything. What would cause the this to happen, any clues?
Check to see if there are any major hacks. We had a reimport Dr. Dude that someone hacked up and wired the flippers to be on all the time due to some failed components on the power board. It was a nasty hack and I hope yours hasn't been put through the same garbage.
There's no guarantee flicking the relay with your finger will release the contacts if they're welded together.
You should be able to see the flipper relay contacts closing when you turn the game on if the problem is the driver transistor. You could also check for continuity to ground on the metal tab of the driver transistor when the game is in attract mode. That would tell you the transistor is shorted.