Super Spin is an EM?
Ah, yes. The site I just looked at says it was one of the last electromechanicals ever made. You should be in for a treat.

I would like to suggest looking for the obvious and work your way down. Look for burned connectors, etc. Look for toasted relays and such...
But first of all, try to get the machine to "reset" when you switch it on. Some EMs will seem to be "dead" if it can't complete the reset sequence. If you have a bad gear on the motor and the scores can't reset to zero, drop targets can't reset, or that spinning wheel in the upper left can't spin (or some such) the machine may have a failsafe that refuses to let the game go into its "attract mode" (for what they were on EMs). You can even attempt to "reset" the mechanics by hand to see if the sequence progresses further... IE turning the gears on the scoring by hand, ETC.
The good news is that if the machine was stored in a reasonably decent place and was home owned for so long, the problem shold be pretty simple. Relays are still pretty cheap, and unless you have a "custom" part that has failed, repairs should be pretty inexpensive.
Good luck and let us know how it goes!
APf