Hi Jonny,
There are a number of possible culprits, some of which I've listed below:
1) PC Overheating. Try taking the side off of the case, moving the PC away from any radiators or heat sources and seeing if the problem persists. If not, then you've found your problem and can deal with it appropriately
2) Dodgy power switch on front of machine. Check the wiring to the switch and make sure it's not loose.
3) Dodgy connection from PSU (Power Supply Unit - the big unit that you plug the mains cable into) to the motherboad. If you open up your PC, you should see at least one big bundle of cables going from the PSU to the motherboard. Check that the connecter into the motherboard isn't loose. If there are any other cables going from the PSU to the motherboard, check that these aren't loose either.
4) Dodgy power cable to mains. But you said you checked it, so maybe not. Try swapping it for another cable from a known working machine and see if you have the same problem. If you've accidentally rolled a chair or something over the power cable then you may have damaged the wires inside, which could cause intermittent power failures.
5) Faulty / old motherboard. Don't know how old your machine is or how much it gets moved around, but these things do have a finite life. Not much you can do to test this, other than try the PSU on another machine and see if the problem can be replicated on that machine. If it is, then you know it's the PSU and you can just get a new one of a similar or greater power rating. If not, and you've exhausted all other potential sources of the problem, then it could be your motherboard.
6) Insufficient power supplied by PSU. If you've added loads of new internal items to the PC (eg. new graphics card, new TV tuner card, loads of USB devices) then the system might be drawing more power than the PSU can handle. A top end system will need over 450 watts, whereas a middle of the road system might get away with 350 watts. Check the rating on your PSU and then have a think about what the system is using. You can do some simple maths: a P IV 3Ghz CPU will draw up to 130 watts at peak demand, not sure what your gfx card draws, but you should be able to find out on the nVidia website. Sound card should have power requirements listed somewhere too, so will any other PCI cards. Add them all up and see what you get. Then compare to PSU rating and see if it's enough.
As always, ground yourself when working inside the case. I do this by leaving the PSU plugged into the mains as this ensures that the PC case is grounded through the mains cable. Then I just touch an unpainted part of the PC chassis before I start and every so often whilst I'm working.
Good luck with your investigations!
Ben
Ben Norris
December 2006