The tilting out sounds like a switch matrix issue. It could be a shorted column or row. The 74xx chips in the upper right section of the MPU can go bad, especially if a stray wire or lamp socket touched a switch. Put the game into switch test mode, raise up all the drop target and empty the balls out of it. Then proceed to test the switches and see what shows up. If one switch triggers multiple numbers, then you've got a matrix issue.
However, the tilt issue could've been nothing and the game just can't see the ball(s) in the trough. Check switch test to see what you find out. If it can see all balls, it won't start. However, not accepting credits at all sounds like its a matrix problem.