I inherited a Rocket III with training wheels

Welcome mate, Sounds like ignition switch issue/failure if your father in law had issues when he parked it up, try statting it again this time moving the handle bars left to right (moving wires) to see if something else happens
 
Welcome to the forum, I had a loose wire in my egnition and TO rocket fixed it for me.
 
Welcome From Cape Cod. Its a good day to mess around with that Rocket. It will run.
 
Welcome from the Northeast ,sorry about your father-in-law's passing he looked like good ole soul. I've never kept my 2005 out in the elements she's a sensitive gal. Run a can of seafoam through her and make sure the battery isn't dipping below 12 volts...