Cannot shut off

Last night we had trouble shutting off our GE electric stovetop. Finally, we knew we had gotten it ‘off’ – all the burners got cold – but the burner-on indicator-light stays on. I managed to remove it. Its contacts are still electrically live. And we are able to turn the stove on and off and use the burners. But I want to put the indicator-light back in and have it give a true indication. What is wrong? And how do I fix it?