HELP!! '82 380 SEL won't turn over

Very strange:

The security guard in my building recently purchased an '82 380 SEL. Car started and cranked fine.
He complained thathis left-side window switches were reversed. Having some experience with this, I removed the console cover and did the reversal in 2 minutes. Fine.

However, when we turned the key, the starter cranks fine - but the engine won't turn over. Seems like something electrical, but simple.
Could it be some sort of built-in security item, that doesn't allow the car to start if it has been turned on and off too many times in succession? Do we need to wait a while?

Or can it be a fues, like to the fuel pump?

Strange!! Can you help?