I think it's probably a fault within the starter, but I'd take the electrical checks a bit further: What's the battery voltage at rest and minimum seen during cranking (you can do the latter with the jump battery connected if you choose)? You've put in a good earth. Now inspect and wiggle all the other relevant wires and disconnect, clean and reconnect all the connections. That's everything at the starter and the battery and the thin wire(s) to the starter solenoid.Jonathan PS: As well as clouting them when they're sticky you can turn the ignition off, put the car in gear and push it a bit.