Why does my computer just shut itself off?

maybe its overheating,, maybe your cpu fan has died,

first off , get rid of that MC CRAPPY,, that virus software sucks, and is a ripoff,,

secondly,, who knows, you might also have a buldged capacitor or maybe one has blown, and your comp cant hold its power load,,

if its still under warrenty contact your manufacturer and find out their repair policy and send it to them or to one of their authorized repair centers,,

It could be various reason as being highly skilled with computers.

Sense computers can only be used within a certain temperature, once that computer exceeds the amount it can with take, it will just shut off so it wont cause important devices being burned or starting a fire.

Other reasons could be malware, viruses or just a simply slow computer can't handle all the programs you are running to just shut off.

I suggest to try to do a full scan using mcafee.

I could be a boot sector virus,now while you still have time get Avast anti virus. and set it up for a boot time scan,and when you boot next time it will run a virus scan,by the way Norton sucks compared to Avast