Here's a more explicit explanation of what to try next in case the easy fix of reconnecting the plug to the socket on the coin door isn't the problem.
The 110V circuit to the transformer goes through the following: a fuse (the one near the transformer) and then either a switch (m/b) on the S relay or one (NO) on the hold relay. If you manually engage the hold relay (with power to machine) or if you adjust the switch on the hold relay so that it's permanently closed (DO THIS ONLY WITH NO(!!!) POWER TO MACHINE) this would complete the circuit to the transformer (as long as the fuse, various associated wire connections, and contacts on switch of hold relay are good).
Power to the transformer would complete the 6V (lites) and 25V (coils, motor, etc.) circuits via additional fuses (one for each circuit--near front of motor board). And so, once the switch on the hold relay is closed, some lites should at least come on. If they do, this suggests that the circuit that restarts the machine isn't closing when the replay button is pressed. If they don't, then it suggests that there's an issue somewhere between the electrical outlet and the transformer.