Yeah, mine sounds like the starter is smacking into the flywheel but not engaging the teeth so the engine doesn't turn. I would expect the neutral start switch would keep the starter from trying to engage. Of course I have been wrong before...
Also, I backed the car in once so it was headed downhill and had the same problem. I suppose I should double check and make sure the starter is attached securely. If the bolts are loose it could be tipping. I didn't notice anything like that, but didn't actually check it physically. Then I would feel good and stupid, but it would be an easy fix! If it wasn't raining I would go check it now.

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'84 300D Turbo Diesel
San Jose, CA