Sticky airborne residue, a byproduct of normal cooking, gradually builds up on the walls of the oven, the inside of the viewing window and the door frame over time. Left uncleaned, the residue heats up and begins to smoke when the oven is in use. The residue is also responsible for jamming up hinges and causing the light switch to stick.
The switch controlling the light could be defective or damaged. Broken wires or springs could cause the light switch to become stuck in one position or remain permanently off. Although the switch is wired relatively simply, accessing the necessary parts is sometimes difficult.
Disconnect the oven's power, wet a gentle cloth with warm soapy water and wring out the excess liquid. Carefully wipe away any residue around the door switch while trying to avoid dripping water. Place the cloth over the button and pull outward to try and loosen the residue's grip. Clean the sides of the button once it has been pulled fully outward.
Have a qualified technician inspect the wiring around the switch for signs of damage. GE double wall ovens contain a capacitor capable of delivering a significant electric shock, even with the power off, if it is not handled correctly. You might be entitled to free service if the oven is still within its warranty period.