PC powers itself off

your right, replace the power suppy. sooner or later you'll have to unplug HDDs just to get the thing to just turn on.

Check:--

Power Supply

CPU Fan/Fans are working??

Incoming Power ( Spikes/Fluctuations?? )

Event log in Windows

But could be your PSU, memory or graphics card.

Update your drivers.

Have a look at how ur computer deals with Major Errors as well by:

Control Panel -> System -> Startup and Recovery -> System Failure : Post which of those are ticked.

Do a RAM check.

And as you said if those things all check out, then it could be your CPU overheating

The system may have a overheating monitor that will cut the machine off once it reaches a certain point

Check

Power Supply

CPU Fan/Fans

Loose Cards

Incoming Power Supply ( ie attached equipment if any UPS, power boards etc )

Power Options

The power supply obviously works because the system turns on. This is clearly the system overheating, thus having to go through all sorts of stuff to get it to start up again (while it cools itself down). Open the case, blow out all dust that may be clogging the airways and make sure all fans run properly and if not, replace them.

I just experienced something similar on one of my home systems. The system kept cutting off sooner every day with no messages in event viewer or any where else. Virus was updated as well as XP updates. Finally it would not boot past the bios! Tried another power supply, removing boards etc... It turns out it was the CPU overheating due to dust trapped in the heat sinks fins. The fans draws the dust down into the heat sink and the dust has no where to go, the dust is trapped against the motherboard & CPU! Blew the "CPU heat sink" assembly out and no issues since! Hope this helps.

I do warranty work on emachines and the problem has been seen in others but the fix might be hard to pin down. First the problem sounds like the fan for the power supply and or the cpu fan is not consistance in rpm's. This will automatically shut the machine down to prevent more damage. If you have another power supply with the same wattage replace it for a week and see if this prevents the problem from reoccuring if not then the problem is with either the rpm's setting in the bios for the cpu or failure of the cpu fan, which might only run for short times before failing. You could also try to replace the cpu fan to see if this remedies the problem.