Over revving the engine is never a good thing.
First two things that come to mind from doing that:
Though you say a compression test was done, I would be interested to know if it was a relative compression test or individual cylinders.
As to ” Is there something connected to the gear shift handle/transmission/engine relationship that could cause is to stop running and not start.”
If it is a automatic transmission, there is a neutral safety switch.
But that will keep the engine from cranking if it were in gear.
If it is a manual transmission, again the clutch needs to be depressed in order for the engine to crank.