The monitor will make click sounds as it has relays in it. A change of video mode, like when a system reset occurs, will make that happen. When you get the black screen is it hung, or does it just reboot? If it just reboots, then make sure you disabled the auto restart feature in control panel. You will then see the blue screen (if that's what is happening).
Memtest exercises the CPU pretty good too, so heat may not be the problem. You could be onto something with the power supply. They cause more problems than they usually get credit for. They usually start smelling when they're failing though, but that's because many PSU failures are from dead fans and the subsequent overheating that causes.
Did you disable the automatic restart thingy?