I would check the diodes on all coils and switches, have not come loose and that they measure OK. Would also check the capacitors on the bumper switches and targets switches.  I have seen the capacitors cause random triggers even if the caps look and measure correct. You could try cutting one leg of each cap and see if the problem disappears.  If it does, then the caps need replacing otherwise just resolder them back on.

The game restarting could be due the either the caps on the regulator board being faulty or bad sockets on the MPU board.