what type of a stove top is it? (ie glass top or metal rings, gas or electric)

I unfortunately agree with honeychile - your best bet is to try to get a new burner. Is it possibly still under warranty? I doubt plastic incidents will be covered, but they may still be able to help you find a replacement. Otherwise try your local appliance store and see if they can give you a model number and source.

If the part where the plastic is is exposed to the flame (assuming it's gas - or even electric if you cook on high) I'd be wary of trying to salvage it. First off you're going to smell plastic burning from now on when you use that, and if there's any residue left, it could start a fire.