The door switch is perhaps the most obvious culprit for a dryer not starting. If the dryer can't detect that the door is securely closed, it simply won't do anything. Try using a multimeter to detect current continuity. With the door closed and locked, you should get a reading of zero ohms. If not, the door switch apparatus may be worn or damaged. Time for a replacement part.
*GE Appliances technicians carry an extensive parts inventory on their service trucks. In the event a part is not available on the service truck, a follow-up service call may be required.