Win 7 Logs off and Shuts Down Randomly

I'm currently having a problem with one of the computers I recently installed Windows 7 with.
Originally, the computer was logging off and shutting down within 5 minutes of booting up.
After messing with the Power Plans, I was able to keep the computer on for longer but it continues log off and shut down (it just takes much longer for it to do so)

Although I used the Diagnostic Utility in the BIOS (which brought back no errors) and had Win 7 test for RAM errors, it continues to shut down. Although I haven't physically taken anything out, I don't believe this to be a hardware issue. I'm only saying this because before Win 7 logged me off/shut down I was installing updates. A couple of updates into it it decides to log off, but not before it CONTINUES to install updates!

I'm not sure if anyone has come across this before.
And although I don't think it's hardware, I'll list the model anyway:
Panasonic Toughbook CF-30KCP542M (MK3) w/ 4 GB RAM, 80 GB HDD.
Windows 7 Professional (64-bit).

 

Did you check the settings for shutting down when battery power is low and the state of the current battery? If the battery is failing, it might be the cause of this although that shouldn't have an effect if you're plugged in.

You could also check the event viewer, it might give you an idea of something that happened at the time of the shut down.

If updates didn't complete properly, it might be part of the issue.

 

Check the CPU temperature shutoff value if it has one. Does the CPU fan step up and step down for loads/non loads ? Whats paste do have on it and how long has it been ? Arctic Silver 5 ?

If the oses got toasted by updates, F-disk it.

Cheers
3Fees

 

The battery is actually great. I've tested it with another unit and there isn't anything wrong/suspicious going on with it.

Event Viewer has also been giving me errors regarding the 2 cores of the computer being restricted by the firmware (which is understandable as the unit is a built to only use a 32-bit OS on the Intel 2 Centrino vPro, but I have it using 64-bit). I've already tried using a 32-bit OS on a different HD, but it shuts down the same way! I also get Even ID with WMI as the source.

The toughbook doesn't have a shutoff valve.
I'm not sure what paste Panasonic uses. It looks more like a thermal pad than it does paste actually.
Although I haven't F-disk'd it, I tried a 32-bit OS on the computer and it shuts off all the same. It's only when I start running programs does it shut down, but as soons as I leave it alone it stays on.

I'm beginning to think that something is indeed wrong with the unit

Thank you for all the suggestions!