I used Dr. Web's cureit to see if it was a virus or trojan, but it came up clean as I expected. I also ran an adware scan and no adware either.

It's only doing it when I'm doing something more intensive than just posting or surfing the net.  All I've been doing on this thing for 2 days now is surfing the net, copying files from CD and running folder/file searches to locate .zip files that I need to unzip.

The computer only reboots during the copying for files from CDs and once or twice while I was running a search for folders/files. It hasn't rebooted on its own any other time.

Last night I was moving small numbers of files between hard drives and folders and I managed to go a few hours without it rebooting.  I started to copy more files from CDs and when I was on the second or third CD it rebooted part way through the copying process.

"It is good to see ourselves as others see us. Try as we may, we are never
able to know ourselves fully as we are, especially the evil side of us.
This we can do only if we are not angry with our critics but will take in good
heart whatever they might have to say." - Ghandi