Have you checked your temps? The way you are describing it sounds like your system is resetting due to overheating. As you say it happened less frequenetly at first, and has now increased (which could be due to dust build up or dying fans).
I'd suggest you run prime95 / intelburn test and monitor the temps. This will push your cpu to the max and let you know if you are indeed having heat issues.
Worth ruling that out before you look elsewhere.
Another good thing to do would be update your motherboards bios and ensure that your network/sound/graphics drivers are all upto date. You can find the model and manufacturers of your network/sound via your motherboards homepage.
Thanks for the messages guys. I checked my ram and temp and they're both OK. When I take my 5770 out and use the graphics card on my MB everything works fine - no reboots. So it really must be the graphics card.
The computer sometimes even reboots in DOS while booting, so I don't think it's a problem with Windows. Ubuntu doesn't even load with the graphics card - I don't think it reckognises it (seen lots of problem posts about Ubuntu + 5770 online).
I'll keep looking - but any feedback is much appreciated!