I meant motherboard and PSU on cardboard. No CPU or case is needed for this down to 2 item test. All that I expect is to be able to power up and down the PSU via the power on switch.
If that works I add the cpu, heatsink and the speaker. If it doesn't beep in protest I am looking at the 4 possible bad parts.
As to the 4 pin connection. That's called the ATX12V connection and should never be removed as it's part of the power to the motherboard.