Does the player advance correctly for the first four balls of the game? In other words, does it correctly go from player 1 ball 1, to player 2 ball 1, player 3 ball 1 and finally to player 4 ball 1? If so, then the Player Up Unit Step Up Solenoid at the top of @howardr's schematic above is working which means that the first three switches to the Ball Count Step Up Solenoid are working.
And if I understood correctly the game behaves the same for all four positions of the Coin Unit disc too, right?
If that's all true, the one thing in common to all those scenarios is the Score Motor 3D switch in the center of @howardr's schematic. That would seem to be the most likely culprit.
/Mark