Computer randomly restarts/logs off after an extended time.

Hello all. I am having a frustrating issue with Windows XP desktop computer right now.

For no reason at all, it has been restarting/logging out randomly the past few days sometime during the night and after a few hours of extended time. I am not sure whether it is a restart or log off because I have never actually been awake to witness this actually happening. I love running virus scanners and Torrents when I'm in away, but when I wake up all of that just disappears. I tried checking "Power Options" in the control panel and I have tried checking "Display" in the control panel, the most popular suggestions, but none would work. What should I try this time? I would really love to get this fixed.

On another unrelated note, I am having an issue with my laptop that has been going on for over a few months now. When it sits by itself, it randomly freezes up, but it's still on. I hear it humming, the lights on the keyboard are on, the processes still go on, but the screen freezes and the wireless light turns orange instead of its normal blue. This is a Vista laptop, btw, so I guess this is KIND of in the wrong place.

Thanks a lot for any help you may have.