The "burner on" light stays on all the time
Here are parts using the given model number.
http://www.appliancepartspros.com/partsearch/modelsearch.aspx?model=JBP350H2WW
I cannot find info on the given model number so please check it.
Also it may shooew up in the Matching Model Numbers section.
Most likely it is a bad infinite switch for that element.