Welcome to Pinside!

Definitely worth fixing - either to enjoy or sell. Egg Head is a great looking game and can definitely bring the $$$, but I would suggest you try it first!

The thing you describe as spinning is the score motor. I'm suspecting you have a stuck switch on the playfield somewhere or the coin door, if it does this from the moment you plug it in/turn it on. If you add credits to the game by hand (the reel in the backbox can be advanced by hand) and press the start button, does anything happen? The first thing that should happen would be that some things would reset and the reels would attempt to go back to 0.

When the score motor spins you don't happen to hear anything else activating as it does that, do you?

Could also be stuck in a reset loop but ehh...

Since something is lighting up that means one of the two major power relays is working (120V hold) which also lights up the backbox, and since the score motor is running I would be inclined to believe the 30V hold is also working fine. So, I'm assuming both the backbox and playfield are lit?