Hello
I can be surfing the Internet or listening to music and my computer keeps randomly locks up and when it does it I have to switch it off at the mains and back on again. I have already tried removing the cmos battery, Reinstalling windows. I have also tried a new power supply but still it makes no difference

My Spec is
Asus A7N8X-LA Motherboard
AMD ATHLON XP 3000+
512 MB of DDR PC2700
60GB HARD DRIVE
400W Power Supply
NVIDIA GEFORCE FX5200
DVD ROM DRIVE
Microsoft Windows XP Media Centre Edition

Check the temp readings inside the case and of the various components, like the CPU. It may be shutting down once the temp gets too high.

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When was the last time you dusted it? a thick coating of dust can reek havoc on the hotter components (especially graphics cards- make sure you dust inside the plastic casing that surrounds the fan (assuming you bought one with an attached fan)) It could also be that one of your fans- maybe the one cooling the CPU- has failed, causing your system to overheat.
If its not either one of those two things, you could have an issue with your motherboard, which is programmed to shut down in case of overheating; if so it would probably need to be replaced.