Recently I started smelling a funky smell from my computer that smelled like burnt plastic. Assumed it was the heatsink gone bad due to big dust bunnies. Cleaned out the dust bunnies got a big cooler, used good paste but when I removed the old one I put small scratches on the bottom. Didn't bend anything. The new big cooler won't allow for the fan to attach due to the proximity of the PSU (so no fan is plugged where CPU fan is marked). Before I put the new cooler in, I was able to get into my computer to post and get on the web. Started to smell something again and before I could finish researching the web about the problem it shut down. Got the new cooler attached and then it would turn on no beeps, fans (no post) (only on for 2 seconds) then it turns off. Then on again on its own, then off again, then on again. The only way to make it stop is to flip the switch on the PSU or unplug it. Thought it was the PSU but bought a new PSU. First one was a OCZ 700w and this one is a OCZ750w. My mobo is a LGA 775 Gigabyte DDR2 with an Intel 2 Quad Core. 4 GB of ram (2 sticks). Nvidia PCI 2.0 Video Card (forget the number but it has its own heat sink but not power plug for it. Never needed one for it. After putting in new PSU same issue on and off and then on, then off etc... I pulled the memory out and then one by one put it back in. Same issue with or without memory. No beeps. The smell is gone though so that is no longer an issue. The smell disappeared with the new heat sink.
Generally speaking, you want something plugged into CPU_FAN so that the motherboard can inform things about the heal level in the processor so they can adjust themselves correctly to increase CPU heat levels by, say, increasing the fan speed.
My gut feeling before I read the description was bad RAM or RAM not pushed all the way in the slot (sometimes it looks like it is and it really isn't).
Then you talked about burnt smell which is usually a bad PSU. You said you replaced that, though, and I have to try and assume the new one is good.
After I read the whole description it started to sound like you damaged your CPU physically, though.
Also, incidentally, you should get a case with a bottom mount PSU like the Antec 300 Illusion instead of whatever you have. The CPU cooling system shouldn't be negatively be impacted by the PSU mounting in a current case.
Cooling technology has come a long way since the days of top mount PSUs.
a few thoughts;
1) Re-seat the Ram
2) Take out the CPU and make sure that you did not accidently get any thermal paste on the under side of the CPU. It happened to me, even when I though I was being super careful. Thankfully no harm done to my C2Duo, just wipe it off and all was well again.
3) Reset CMOS/Bios/Uefi. Sometimes (especially after a power spike) the mobo can get corrupted, and just needs to be reset to get things working right again.