GE built-in oven

The oven started beeping and displayed the error code F0. I replaced the controller and every thing was OK for almost a year. It started beeping again. The warranty on the controller yielded another new controller, but after a week or so it started to beep. I disconnected the ribbon cable and after 4 minutes it showed the error code F0 on the lower oven, and after another 5 minutes the upper oven also displayed the F0. I put the second controller back in and with the ribbon cable disconnected I got the F0 on only the lower oven. I had discovered that if I disconnected the J6 connector disabling the lights and the convection fan the beeping stopped and the ovens still functioned.

Can anyone suggest what the problem might be or tell me a way to test for a diagnosis of the problem?