Sounds like the board is failing to post.
Strip it back to the basics to reduce pull on psu, 1 piece of ram, no drives connected.
If that fails, pulll all the memory and see if you get an error beep, thats ok.
If so, put back in 1 stick of memory and pull graphics card unless onboard, if you get error beeps thats ok.
If you get this far, reseat heatsink and apply new thermal paste.
If no joy, motherboard is fubar.
As for 20 pin psu in 24-pin socket, if this is the original psu, don't worry, if not, could be not enough juice to motherboard.