I had a slowly worsening problem with one of my '80 300 TDs; the starter gear often failed to engage the flywheel, or when it did engage, would fall out and spin freely before the engine could start. A month ago I removed and tested the starter; it acted the same as my (used) spare. I reinstalled it and the problem was not changed. Then I cleaned and refastened ALL electrical connections involved, including the frame-to-transmission ground cable. This solved the problem.
Steve

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1980 300 TD

1997 Dodge Pickup/Cummins 5.9 12-valve