I reset the AX relay first,that stops the score motor running,then it will play,not sure if it is set for 3 or 5 ball but the burnt coil is the game over relay.. 
Sounds like it is a 3 Ball game (set in the head), and the GO Relay is not being activated as the coil is not working.
I agree - not far off now. You could activate the GO Relay After the 3rd ball, and then the "Game Over" light will turn on with the "Match" light as well
