Frigidaire Gas dryer, it turns on and hums when I try and use it. I taped the door sensor and turned it on and then gave it a hand spin, and it started up. Is my motor shot?

Sure sounds like it

It could be a bad start capacitor, too.

Without running it through a diagnostic testing, or seeing if an error code displayed (if you have a digital display) it is very hard to 100% say if it the motor or the capacitor. Though I agree with both parts may need to be tested and looked at by a professional, I would first start by resetting the unit at the household circuit breaker. Give it about 10-15 minutes, then retry the unit. You could just have a stumped timer in the unit. After that see if you can manually rotate the drum again with or without any noise or humming. Then try another cycle with clothing inside. Watch the performance and see what happens next. Let me know if anything changes, for better or worse.