This is basically how a PC turns on.
1) You press and release the power button which momentarily shorts the PWRSW pins together, telling the motherboard it's time to turn on.
2) The motherboard internally connects pin 16 (PS_ON) to a ground (COM) on the 24-pin connector which turns on the PSU.
3) The motherboard then senses if the PWR_OK signal from the PSU on pin 8 is good, if it is, the motherboard keeps pin 16 grounded and the PSU stays on.
You should disconnect the
24-pin connector and use a jumper to connect pin 16 (the only pin with a green wire) of the 24-pin connector to a COM (any pin with a black wire, but there's one on each side of pin 16) to manually turn on the PSU..Scroll down to the
PSU Paper Clip Test..Then use a digital multimeter to check voltages on the 24-pin connector and the 4/8-pin ATX12V connector to the CPU..You can buy a cheap DMM for around 10 bones at some places.
What it boils down to is that if the PSU doesn't turn on, it is bad..If the PSU turns on and the voltages are good, the motherboard is bad..You could also swap out the PSU with a known good one.