First get a meter and check the power supply voltages to make sure they are in spec. That's the first thing you do with any repair of this nature.

Here are the pinouts for the main power connector CN1 (power supply generation differences are listed). Pins 1,2,3 are the pins surrounded by the "notches" on the sides of the connector plug.

CN1 pin 1: 18 volts from bridge BR1. This goes directly to power supply connector CN4 pins 5,6,7,8 for the lamp matrix. On games Checkpoint to Guns N Roses, this also supplies voltage to the power supply's voltage regulator VR1 which creates +12 volts for the DMD, going to CN5 pin 5 (for games with 128x16 and 128x32 dot matrix displays only).
CN1 pin 2: 32 volts from bridge BR2 for the solenoids.
CN1 pin 3: 32 volts from bridge BR2 for the solenoids.
CN1 pin 4: High voltage for the displays (games with alpha-numeric and 128x32 displays only).
CN1 pin 5: Not used.
CN1 pin 6: Goes directly to power supply connector CN3 pins 1,2.
CN1 pin 7: High voltage for dot matrix display (unused on pre-dot matrix display games).
CN1 pin 8: Not used.
CN1 pin 9: High voltage for dot matrix display (ground on pre-dot matrix display games.
CN1 pin 10: 9 volts AC to power supply bridge DB1 for generating +5 volts logic. It is also used to generate the +12/-12 volts for the sound board, by doubling up with pin 11's 9 volts (to get 18 volts).
CN1 pin 11: 9 volts AC to power supply bridge DB1 for generating +5 volts logic. It is also used to generate the +12/-12 volts for the sound board, by doubling up with pin 10's 9 volts (to get 18 volts).
CN1 pin 12: Ground for pins 10,11.

http://techniek.flipperwinkel.nl/desega/index1.htm