One hotplate stays stone cold, or sits at full heat whatever the dial is set to, while the rest of the top behaves normally.
Usually: Either a radiant or solid element that has gone open circuit, or an energy regulator whose contacts have burnt and welded shut.
On the visit: We draw the cooker out, test that element for continuity and watch whether the regulator actually cycles, then change the failed part and run the ring through its full range.