Let me first tell you that there are a lot of reasons for your problem.
To start with , it may be due to a virus.
But, as you have thouroughly scanned your computer with Norton 360, it is a remote possibility.
Still, let us confirm if it is due to a virus.
Start your computer and press Windows key+R.
and press enter.
In the new window, click Services
tab and tick Hide All Microsoft Services
and click Disable All and tick only your Norton 360 Services
and click Ok
.Immediately restart your computer.
While windows is loading, keep tapping F8
to enter Safe Mode(Do this even before windows logo appears).
Once you enter safe mode, check if you face this shutdown problem.
You will not be able to connect to internet while in Safe Mode.
After checking for some time, if the problem doesnt occur, repeat the earlier steps and select Enable All
and restart your computer and login normally and post me the results.
You can reach this link by using this URL:http://www.justanswer.com/questions/3o5dr-i-believe-i-am-out-of-memory-space-my-computer-keeps-shutting
Save it in a notepad file on your desktop.
Edited by Renju on 6/26/2010 at 4:45 PM EST