[MisterW]

It sounds like it is most likely a power supply or motherboard issue. You said that "giving the machine a rest" seems to help. One cause of the problem could be bloated capacitor(s) on the motherboard. If this is the case, the computer would turn on normally, but either freeze up or not work after a short time. Turning it off, allowing the damaged capacitors to discharge, then starting up again would cause the machine to do the same thing. Turning it off and back on right away would result in a nearly immediate freeze/malfunction.

If this sounds like it could be your situation, you can open your computer and look on the motherboard for small, cylindrical shaped pieces (capacitors) and inspect them for a bloated shape. If you find suspect bloated capacitors, the motherboard is your most likely problem and you'll need a new one.

-MisterW