Does the payout relay coil look ok, not burned? If you have a meter you can check the coil's winding for continuity, should have a small resistance reading between the coil terminals. Do this with the machine unplugged, or at least turned OFF.
Or you can use a meter to see if the coil is getting power when it is supposed to be activated. For this you can attach the meter leads to the coil's terminals and see if voltage is there when a payout is supposed to happen. For your machine I don't know if this is AC or DC voltage, probably AC. If the voltage is present but the coil does not work then it's bad. If the voltage does not get to the coil then check whatever sends the voltage to the coil.
On EM machines a lot of times the problem is related to switch contacts, so a good cleaning to all of them might get it running again.