That link for a previous answer that James posted in the above response has some good suggestions. Your details indicate that you probably already tried most of those solutions. I recommend that you try one more cleaner that may work. The Bar Keepers Friend kitchen cleaner is approved for use on that type of ceramic cook top. It will not harm that surface. I recommend that you buy the powdered version of that cleanser and see if that will remove the black discoloration. You may need to make a paste using that powder and a small amount of water to clean off that black stain. I have had good success with that product. If the Bar Keepers Friend won't remove that black discoloration, then the cook top will probably need to be replaced to resolve this problem. Here is a link for a brief repair video that shows how to complete that task:
Electric Range Main Top Replacement
. If you are confident that you can complete that procedure yourself, then you can order that replacement glass top from the
website. Use the full model number of your range to access the parts list diagram and order the correct top.
If you need more help, reply with additional details and we will assist you further.
If you get to the point where you need to have a service technician replace that glass top, you can schedule service through this link:
Sears Home Services