Well, although I am a decent handyman I am not an electrician, so I got some help with testing the various contacts/circuits, nothing showed up. Since the switch seemed to be all right, the only other things that could have gone wrong was the element itself, so I ordered the element and changed it, .... Voila !! ... that fixed the problem, now the element works and the warning light stays off once the surface cools down.
One advice; before taking the old element housing down make a note of which color wire connects to which terminal, because if you don't and take everything down figuring out the wires could be a big problem.