I would have shitcanned the SOB by now. I'd order a completely new motherboard. I feel your pain though...computers can be incredibly annoying to put together if something like this happens. I just thought of something:
I think it could be your processor. I fixed a PC last summer that was doing the exact same thing...I put my extra processor in it and it fixed it immediately. That's how I fix all of my computers...I trade out every single damned part in the system until it works, even if it means trying another motherboard. You said you've tried two motherboards and two RAM sticks and it still does it. That points to another component, and a PC not even getting into BIOS is a big symptom of the processor being fucked. That's what I'd try next. Not sure how you can try out another processor though; it sounds like you don't have many resources to work with.
-Lasereth