Hello Rawr

Welcome to PCHF
That would sound to me like a power issue. The best way to test would be to try another power supply and see if it helps the problem. If you buy the power supply from a local retailer, they should have a 30 day return policy where you can return it if it doesn't help. If the symptom you listed is the only symptom there is, then I have a feeling it is the power supply.
If putting a new power supply in shows the exact same symptom, then your best bet will be to start by taking out all the peripherals (modem, sound card, network card, video card if you have onboard video, etc.) and adding them in one by one until you start to see the problem occur again. You should also try reseating your memory (take it out and put it back in).
You can also test your memory with Memtest86. Click my link at the bottom of my post. It is a free diagnostics tool. You will create a bootable CD or DVD with it and it will run automatically when you boot to it.
Your testing is going to take days to really know for sure, because you should put each component back in one at a time and test the unit by leaving it off overnight and then powering it back on with just one more component added.
If after taking out all the components, you still see the problem with a new power supply installed, then it is most likely a problem on the motherboard.
I hope that all makes sense. Let me know what happens and we will go from there
