Sounds like a possible relay fault, or even a door switch. I'd go with the relay myself.
It could also explain your convection problem, but that could also be caused by a faulty thermal.
You won't know until you open up the unit and check the relays and switch connections.
You can test the Thermal with a multimeter. Check the element too for continuity, or if it is earth bound and blown a fuse.
Jon, June 2007