A typical 5V or 12V charger that u plug into a wall, will basically be like the auxiliary and standby circuits in a computer PSU.
The Aux voltage supply is usually like 12-15V, and it derived from the rectified mains voltage. It makes the low voltage to power various control chips and mosfet gates, on the hot side. It also makes the 5V standby on the secondary side. That runs the control chips on the secondary side, and the power button on the PC is tied into that.
When the PC pwr is pressed, basically a 5V standby circuit, uses an opto-coupler to tell a chip on the primary side, to start the circuits for the PFC boost converter (if it has it, most PSUs of any size these days do), to double the rectified mains voltage. Then feed that to the main converter, which on the other side of the big transformer/inductor, make some stepped down voltage, closer to the desired output.
There's different ways they get to the final 12V, 5V, 3.3V, -12V, but sometimes it's just stepped down, rectified, and LC filtered to a smooth level. Some use another stage of switching DC-DC converters, to take 12V and like a buck converter, step down the voltage. That's what the 1 in the schematics does.
Well on your computer, did you try running any benchmarking/stress-testing programs ? Try running a shareware program like CineBench, or OCCT. They can use a lot of power for the CPU and GPU, and see if that upsets the PSU.
And have you really narrowed down that's it's the PSU, and not the mobo ? Do u have another PC to try it in ?
You could probe various output cables, (helps to tape some test-leads or wires into the molex connector. The regulated voltages are usually pretty close 12/5/3.3V . 1 of the common things to go wrong, is the output caps, start acting more like resistors, and like a voltage divider, you start to drop too much voltage across the caps, and instead of getting 12.2V out, you get 11V, and the more current being drawn, the worse it gets. That would show up easy.
There's a few control chips, that monitor different voltages/currents. If stuff gets too high/low, the PSU can shut itself down.
It would be nice to see on an oscilloscope, what happens to the various voltages, when it shuts down, some problems will make certain voltages die before others.
There's clues to look for all over the place.