This is a total long shot, but have you considered unplugging everything (including the foot pedal), let it sit for a bit (off), then plugging everything back in?
If the problem still happens, then I would be tempted to sew without the foot pedal to try and get more data. (Is there a way to sew with just a switch or button on the machine?) This could potentially tell you if the machine is the culprit or some bizarre wiring thing with the foot pedal.