Dennis,
Something is being lost in translation here! If you can turn your key to START and have the engine turn over, you DO have a solenoid type starter, it just has some wiring glitches.
I think Cletis had the right idea from the git go! Your ignition isn't being powered in START. I don't know exactly how this would be accomplished at your aftermarket key switch, but your solenoid should have a second small terminal which is know as the 'relay' terminal. When the solenoid it engaged and starter spinning, this terminal becomes powered and sends voltage to the ignition system for a START.
When the key rolls back to RUN, power for the ignition is then supplied through the keyswitch as the little relay terminal is no longer powered.
Does this make it more clear?
Stuart
