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Strip the solenoid. You will probably find that the copper contact strip mounted on the solenoid shaft is corroded or arc burnt to an extent that it doesn’t make good contact with the fixed pins.
Which obviously points to the motor.
I used a refurb kit on the starter and I always thought it sounded slow, but no nasty noises.I probably need to take the starter motor off (or hook a battery directly to it) and see if that's the problem.Would a jump starter pack work instead of a battery?