Quick note: Anti-static bags aren't very safe to run on dude. The reason they have Anti-static properties is because they are conductive
! Ummm...don't do this again...you're making me cry already
Use a piece of cardboard.
CPU may have thermal tape, ceramique, or the paste just dried on there. How do you take it off? Very carefully. It could be that your proc is overheating due to this paste breaking down and just plain not working anymore. These things being hot crash quick...often prior/during the POST in worst case scenerios. So, it may be worth getting it off...but let's leave that for last. Check everything else first, then fumble with that damn thing. I know they're hard to get off sometimes, and it's just a PITA. I know of nothing besides xylene based stuff like acetone or pure alcohol and a little TLC to get it off. I, luckily, have a spare socket I ripped off an old board that helps hold these if I run across a stuck one. But generally, I just soak it down in contact cleaner, then keep it wet with alcohol during the removal. I twist the CPU the other direction of the HS, but sometimes need a help of a screwdriver. Again, it sucks. Stuff save to use from Arctic Silver's site: "Use xylene based products (Goof Off, some carburetor cleaners and many brake cleaners.), acetone, mineral spirits or high-purity isopropyl alcohol."
Having the CPU out and it running doesn't really rule out the memory. IIRC, the ram-check process needs the CPU to do the test. If I'm wrong, then the BIOS does the processing. I doubt it though as I believe the BIOS only has the instructions, not the processing unit. And it basically can't even attempt to POST without the CPU.
My first guess was that the Power Supply headed south, so I'm going to stick with that instinct. Don't have another to try, do ya?