I believe on Gottlieb machines, if the slingshot switches are stuck closed, the machine removes power from the coil. Look at the two metal blade sets sticking up behind the rubber. Each set has 2 metal blades. They should be gapped. If they are touching, they need to be adjusted. A ball hitting the rubber should close the switch.
ANY ADJUSTMENTS SHOULD BE MADE WITH THE MACHINE POWER OFF.
Might be easier to see with the plastic removed from the sling.

Next I would inspect the coil, look for a loose wire, broken wire. Does the mech move freely by hand? Any burn marks or discoloration on the wrapper? If all checks our underneath, it may be a board issue.