Looked at the diagnostic help on Appliance Parts Pros.com and the start switch was the problem, but only 25% of the time, so I was a little concerned it may be a different problem. The switch was reasonably priced, so I ordered it and it arrived in two days!
It was very easy to follow the repair video, however, my GE Gas dryer had a lot of screws rather than 2 screws and tabs on the model in the video, so it took a little more time to open up. After turning off the gas and unplugging the dryer, inside the top panel it was easy to start disconnecting the old switch. I immediately connected the wires to the new switch as they were disconnected from the old switch. The new switch snapped into place and I plugged in the dryer before closing it up, just to see if the part was the fix.
The first couple of times I tried to start the dryer, I got the same buzz and no drum movement, so I suspected something else was wrong. I looked at the APP website for help and decided to check on the next thing which is the door switch. The video for this repair was great, you open the door, have someone press the door switch and turn the start button, if nothing happens the person spins the drum. If the drum doesn't keep turning on its own, then the door switch is bad. In my case, the drum started turning after a push, and we tested it several more times, so it may have needed the push after the new switch up top was installed. Closed up the top, opened the gas valve and the dryer works great now!