car will not restart after driving. Starter spins but will not engage.

Remove the starter and "bench test it" using a battery and jumper cables.

If your starter spins but does not engage, your most likely culprit is not electrical but mechanical. Try gently tapping on the housing of the starter motor (not the smaller solenoid) with a hammer while the car is off and then try again. If this works, replace the starter as soon as you reasonably can, as the internal components are beginning to bind.