Original post by: Chris Green ,
You could start by checking some of the fundamentals that the mini might not start without, like the Interconnect board, or something really straightforward like the power button. I have a mini that had been quite unstable until i took it to an apple store. I wrote down some numbers for parts, and took a few pictures before i sent it out and when i got it back it showed evidence that the logic board was removed but not changed. I am not aware of any way to test the logic boards, but your best bet would be to make sure that there are no types of obstructions to the interconnect board slot and no scratches/obstructions on the motherboard. you could try and run it "barebones" on a table laid out so that if some kind of case metal is shorting out, it won't do so. But other than that you would need some way of diagnosing the problem.