How do I isolate the problem with my logic board?

I have a 2006 macbook pro, and over the many years it slowly started to overheat until the typical GPU problem kicked in and the screen became fractured and the computer unusable. I baked the logic board, and it worked again, but only for a couple of months before the same problem repeated.

So I baked it again, applied Arctic Silver 5 thermal compound, and upon turning it on again, the hard drive would make mounting sounds and within 5 seconds the fans would be going at full speed, but nothing more. The display would show nothing and I would hear no chime.

I figured the board had had it, so I ordered a replacement from a 99.7% rated seller on ebay with tens of thousands of feedback points.

Upon installing the new one, I turned it on and had the same result. No display, no post, and high speed fans.

So now I am thinking that either this logic board is a dud too and I need another replacement, or that there is something else wrong with my computer other than the board.

Problem is, I can't imagine what else it could be.

Does anybody have any advice for me?