The usual suspects for a no start condition are the rotary start switch, the timer, the door switch, the idler pulley switch, thermal fuse, and motor. A little time with a voltmeter under the hood and the GE will be good to go for a long time again. Quick tip: some of those dryers have a big honkin fuse by the cord terminals.
If I ever get into a GE dryer, I always check the drum support sliders. By far the number one prime suspect.