My indicator lilght stays on even when the burner is off.

Could be an earth fault, or wires rubbing, maybay heat sensor and light will go out when job cool

When the oven lighting mechanism lights the gas the flames heat a temperature sensor that, once hot, increases the pressure in the sensor's copper pipe and opens a safety valve to allow gas to continue to flow (It's made like this so, if your flame gets blown out, the sensor cools and cuts off the gas supply, making it safe from gas leaks). These sensors occasionally fail, and very sensibly "Fail safe" - No pressure in the sensor pipe, the valve won't open and there is no gas to the burner.

If you take a look inside the oven at the back where the burner is, you will see the sensor, usually the bit that is in the flame is cylindrical, about an inch long made of metal about 3 or 4 mm thick, tapering at the end. It will be held in place by a nut that fits on a thread at the base of the sensor. Running from the sensor is a copper pipe that runs to the cutoff valve. Unbolt the sensor and withdraw it from the hole it is mounted in, trace the copper pipe back to the valve (where it is usually screwed into the valve with a 10mm connector that looks like a car brake pipe connector. Unbolt from the valve. These sensors are widely used on most gas appliances (Boilers, gas fires, cooker hob burners and patio heaters all use the same kind of sensor). You should be able to get a replacement from any gas appliance service agent. If you go into a shop, take it with you. The only thing you need to do is make sure the replacement you get is long enough. If you are offered one that is slightly longer, that

Instructions

1. Access the burners inside your oven by removing the access panel in the front of the oven or by opening the broiling drawer, depending on your particular model.
   
2. Determine if the pilot itself is lit, since some ovens have a small flame on the pilot at all times that then grows and extends to the burner when the oven is turned on. The lack of a pilot flame indicates the oven thermostat is malfunctioning or there is a problem with the gas hose. Check the pilot itself to see if it is clogged with debris or grease that could be preventing the flame from staying lit.
   
3. Determine if the pilot flame will grow if it is lit by turning on the thermostat. If the pilot flame doesn't extend, the thermostat itself likely needs replacement. If the flame is extending but the gas valve is not opening, the safety valve could be dirty or defective. The flame should be blue in color. A yellow flame indicates the pilot is dirty and is not burning hot enough to get the main burner to ignite.
   
4. Light the burner on the top of the oven with a match if the igniter doesn't appear to be effective. If it lights manually but will not light automatically, the igniter is likely faulty. Do not do this if there is a heavy smell of gas in the kitchen, since there could be a risk of a fire. In that circumstance, turn the oven off, ventilate the room and call a technician.
   
5. Listen for any sounds of gas hissing or a clicking sound indicating the oven is trying to turn on. If there is no response from the oven at all, the gas may not be functioning properly and will need to be examined by a technician for safety purposes
   

Tony, this sounds like you may need to have a new burner switch installed, it is called an infinite switch. If it is for the dual burner, make sure you tell the appliance parts store this so they can order you a dual infinite switch.

I have a GE stove which I purchased in 2004, and it is doing the same. I heard beeping coming from the kitchen in the middle of the night . I went to the kitchen and the oven was on by itself. I have been unplugging it when not using it. Maybe this could be a recall.

Are you talking about the cook-top part of this unit or the interior of the oven? If it's the top part, your infinite switch is out. If it's the interior, it's one of the elememts. If you will give us a call as soon as you get a chance, we'll make sure and get the correct part out to you right away to get this repaired. We look forward to working with you and getting your oven fixed BEFORE Thanksgiving. 972-859-0929

A sensor on one of the burners is bad.
Eric

Most likely a faulty burner limiter switch. Not sure if they can be purchased separately from the burner element.
-Dave
http://www.appliancepartspros.com/part_details.aspx?part_id=3767588

yes , hopefully you have a seperate indicator light for each of the elemnts, makes it easier to see which has gone bad, but if yo know which burner you were usins at time of incident then you can assume that it was that elemnet. replacement of the elemnt is required, for a it has a short in the theremistor, not a hazard, more of an inconvience, so i would have it taken careof but no need to rush its not an emergency, its only an faulty indicator, the elmnt is not actually heating

this is a common indication that the ignition module is probably going bad or the flame sensor is not sensing the flame on the burners. There are other, more technical issues possible but this is usually the most common. The "not restart" , if referring to the burners, is an indication that the ignition module has "locked out" the system, usually after 3 failures of attempts to light the burners.