The desktop (tower) PC has been suddenly 'DYING' without notice, after varying numbers of minutes. The CPU heatsink fan stops turning, but a LED on the motherboard stays lit. I experimented with the RAM sims and slots, but got very inconsistent results. I tried to run MEMTEST to get a 'sophisticated' evaluation of the RAM, but the PC KEPT dying before the test ended. I thought I had heard some 'arcing' noise, so my next suspect was power supply. A replacement 'fixed the problem' ONLY while the PC was left on its side; when it was turned upright - as a tower is supposed to be - the problem returned. Any suggestions what loose connection to look for ?It has to be the power supply Arcing noises should only be able to come from the power supply (especially considering that the computer still works) and the random power cuts fits.

You could open the power supply up and have a look for burnt/leaking components or loose exposed wires. But I would have to recommend that you don't do that unless you know what you are doing. Inside that BOX is the mains voltage side of things and the CAPACITORS inside it can hold a dangerous charge.

Recommend that you stop using that power supply (unplug it from wall socket) and buy a new one.

What is the history of that power supply anyway? Have you added more load to it recently?