I think this belongs here....

I have installed Debian 6.0.3 amd64 onto my AMD dual core Athlon PC (2GB's of RAM), it is dual boot with Windows XP pro as the other OS.

Debian will boot OK and will run OK but randomly restarts the system as though you have pressed the reset button. So you get the full BIOS screen, then Grub Loader then it boots into Debian again.

The reboot is not consistent, It has happened with no applications running, while browsing or with a terminal window open. Some times it happens really soon after loading Debian, some times after a long time.

Windows runs - well as perfectly as you can expect from MS windows, in that it does not reboot the hardware but does occasionally have problems....

Any help on why this happens or how to fix it will be received with thanks !

Boot to a LiveCD and select memtest from the boot options. Let it go through the process at least once and see if it flags some bad memory addresses. That's where I would start anyway. Linux tends to be far less tolerant of bad memory than Windows is.

Ran a memory test and it passed all the way through, booted to Debian opened up a terminal window and it self re booted again, very frustrating

What kind of behavior is it displaying in Windows?

It might be a power supply going bad, motherboard (Possibly bulging capacitors), or the video card. Or maybe even a buggy graphics driver.

Check in the /var/log folder. Maybe there is some helpful info in there being logged.

Another thing you might try is to run from a Live CD for a while to see if that is stable. From there, you can also run e2fsck on your unmounted hard drive to check for bad blocks and to fix any file system problems. Check "man e2fsck" in a terminal for options.

Hope you figure it out. I HATE those hard to diagnose computer problems.