So, let's see if I have this straight. If you press the start button once for a 1-player game, it will boot up completely and pump ball 1 into the shooter lane. After you play and lose ball 1, the machine then goes to Player 2, ball 1? Then to Player 3 and Player 4? What happens when you lose the ball on Player 4?

I would start by inspecting the operation of the Player and Coin Units on the cabinet bottom board. Those two units have to work flawlessly for proper ball count and player count operation. Check to see if you can manually work the advance solenoid plunger for each unit and they will step the spider to the next set of contacts and stop the spider arms centered on the contacts. Also check to see if any wires are fractured off either the Player or Coin units. Sometimes the spider will be off center on the contacts and wonky behavior will result.

L