In addition to Gavin's suggestions, the Solenoid Driver board probably has an old 5Vdc Capacitor (C23). It is the big capacitor. These develop a problem where they do not supply a stable +5V to the MPU. Another consideration is the MPU board. If there is any sign of corrosion around the bottom left hand side of this board, then the reset section will be unstable.

Another suggestion would be the diode on the start button can sometime short against the door. Check that as well.

Back to the connectors - Top RHS connector on the Solenoid Driver Board - J5 - Give it a wiggle during a game. There could be a broken connector pin.