58 Ranchero 292 3spdOD Starter engaging in Run position

[Pamlico]

Hi fellas! It's me again with more problems! My Ranchero don't know when to quit! It all started when my battery slowly failed. It is an old battery which gave me great service. At the last, when it was turning slowly before quitting, the starter would not turn enough to throw out the bendix and the engine would try to turn even with no key in it. I figured out that the solenoid was shorted and would unshort with a few taps. So I put a new USA made solenoid on it. Then it would try to start when switched to the run position (not START). Since then I have replaced the battery and ignition switch(USA made). It STILL turns the starter over by just turning the switch to Run(not Start). Any ideas on what's going on?
Thanks,
Jeff