A few weeks ago my Built-in Oven stopped working, I would set the temperature (so you see the target temp in red and bake <on>) and it would sit there for 10-30 seconds then go back to the idle (clock) state. I tried the various modes but the best example is convection where I set it and the fan starts and 10-30 seconds later it just turns off and the screen returns to the clock. As far as I can tell the elements are not working (don't feel hot to the touch) but it doesn't stay on long, there are no errors messages or any other indication, it acts as-if I pressed the CLEAR button essentially.

I tried the breakers (both at the power box and the ones near the unit) and it didn't work, so I left it there for a week. After I tried it (by simply flipping the breakers) again and miraculously it worked ... for 3 days ... since then I have been unable to get it to work again ... same as the original problem.

The unit is a built-in over/convection, on the unit it says (GE profile) and the user manual has the following on the footer of the cover page:
300A500P34
WB60M778
The unit came with my home and I would assume it is at least 5-10 years old.

I would like to try and exhaust my options (DIY) before calling a repair guy (going to cost more than the worth of the oven) or buying a new one (this one is too small so I was hoping to buy a bigger one when I renovate my kitchen - in like 100 years :)).

Any ideas, tests, recommendations would be greatly appreciated.
Thanks,