My car has developed an intermittent problem. About one start out of 30 it fails to crank. I've traced the solenoid wire up to a terminal block on the passenger side to crank the engine independently from the starter key. When the car fails to crank, jumpering here to +12 causes sparking, but the solenoid does not engage. I took the starter out and had it rebuilt by the local shop. They replaced the solenoid and brushes...but the problem persists. When this happens, when I whack the starter, it will crank again. My guess at this point is the ring gear has a few bad teeth that sometimes coincide with the starter drive
(like a roullette wheel)....

any suggestions are appreciated!!

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