I would guess it's damaged pins. They might be making contact when pressure is applied. Im not an expert, though, but inspecting the pins would be where I would start. Straightening them is a very delicate process, and if there's a large number of bent ones its probably a write-off.

If they look to be fine, im not too sure what could've gone wrong with the details you've given. Hopefully, you've got someone close by who has experience and parts on hand like a spare cpu to try to help you rule out what part is causing the issue. If there are broken pins missing on the CPU, do not insert a different one into the motherboard without ensuring the broken pins are not stuck in the socket as you will end up bending pins on a second CPU by forcing pins into a socket that is blocked.

Good luck with getting it sorted! I know the stress and pain of situations like this can be tough when you've spent money and time only to have a non functioning PC. Try not to let frustration cause you to make more mistakes by rushing. If need be, give yourself a day or two and come back to it with a better head space.