Oh I remember your post from
this (link) thread sorry to leave you hanging
but it makes more sense now.
Have you tried the standalone PSU test? That would be a good first step (with both the new / old psu) If the PSU can power on and stay on while disconnected to the mobo / gpu and only connected to hdd/cdrom/case fans, it is probably working correctly. Maybe check voltages if you have a meter handy.
The next step would be to try a bare-bones config with only these connected/installed:
-mobo (not really an option lol)
-psu (plug in ATX / +12v / GPU as usual)
-cpu (and HSF of course, connected to fan header)
-mem (maybe one stick at a time then both in various dimm slots)
-GPU (don't forget the hdd or pcie external PSU power if needed)
-keyboard (need to get to bios in case it works)
-power-on header (from case)
-speaker header (from case)
give the BIOS a jumper-reset, then give it a go. Hopefully the screen will wake up and you are happy
If nothing still, you can remove the memory / gpu / cpu and see if you get the respective beep codes.