[scarps68]

Well life got in the way, but I was finally able to get out to the shed. Here's what I found. There is a heavy gauge wire going from the + battery to the solenoid. From the solenoid, heavy wire goes to starter while smaller gauge wire goes to the ignition. Another wire runs from the starter to the push button.

I ran jumper cables from the battery to the solenoid and the push button would turn the starter, but not enough power to turn the motor over.

So to me it sounds like the starter is fine, but the PO did some crazy wiring. Is there a way to simplify and fix the problem?