One of thefour burners in my GE brand old time stove blown up.I changed the fuse.But, still the 'on' light remains on even it's switched of.BUT NO HEAT.What can I do?

I suspect the green light only indicates that the thermostat control switch is closed delivering power to the heating element.

The heating element itself needs to be replaced.

You need to find out why this is happening. Guessing does not work due to the complexity of the circuits. In order to know what to do it is necessary to get the model and serial number and maker of the stove. When I know this I can send you a schematic and you will know how to test it with a volt/ohm meter. Without using a meter one cannot know what to do, and as I said one cannot guess unless you want to spend hundreds of dollars replacing all kinds of unnecessary parts and still not be able to fix it.