It would be nice if you could get it to happen again...

While it's 'slowly turning over' of its own accord, open the hood and pull the small wire off the solenoid. It should just be a spade clip. (small wire powers solenoid, biggie wire powers starter which, of course, is switched on by the solenoid).

If you pull that wire, does it stop turning over? If so, chase said wire to the ignition switch to make sure it's not making contact with any other 'hot' wires along the way. Most likely places are at the starter (most likely, check for frayed wires, a dropped penny or washer, etc), or at the back of the ignition switch, in that order. (this is the wire that will eventually go to your new starter button)

If it doesn't stop turning over, I'd suspect a sticking solenoid.

I seem to recall having the same issue, when the battery was very low. Why a low battery might cause that, I can't say. Perhaps the starter gets locked into the ring gear on the flywheel, and since the car isn't starting or even firing, the gear stays engaged, therefore, solenoid doesn't kick back, and it keeps providing power to the starter. When the battery is good, the car starts up (or even fires), and there's enough action between the gears that their disengagement is easy. Just a guess, and I'd call that a sticky solenoid anyhow.






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-Matt I ♥ my ♂