motor starter question- any electrical types out there?

What I'm calling a motor starter is a separate box with solenoids in it which are triggered by low current 110v circuit so you don't have 26 amps going thru your on/off switch. What you are saying is there is something inside the housing of this 5hp motor to spin it up to running speed, like a commercial jetliner using APU gases to spin the turbines? Never heard of that.

This is simply a glorified relay/ contactor. They usually have overload protection. Might be as simple as the stop switch gone bad, or the actual solenoid is sticky.

To troubleshoot break the "stop" contact wiring and add a temporary test switch so you KNOW the stop circuit is broken and retest. The stop switch will be "normally closed" that is when not pushed the stop switch is closed. When you push it, the open breaks power to the contactor relay coil