Step 2: The Suspected Cause
The problem is pictured below.(the second image, silly) Those two X-shaped pieces of metal are what try to hold the heatsinks onto the CPU and GPU. Problem is, they aren't springy enough to do the job. The heatsinks have a tiny amount of wiggle room, and the motherboard is free to warp from heat. That prohibits proper heat dissipation, and allows the processors to break away from their connections. I blame bad design from Microsoft's need to get the 360 out before the PlayStation 3. But now isn't the time for blame, I bet you're about ready to buy one of those Blu-Ray players that come with gaming functionality.
So now we've determined that those "X-Clamps" need to go. The next step lists parts needed.