The computer starts up and runs for less than a minute before shutting down or locking up.
This is a symptom of:

A.
Overheating.

B.
Incompatible RAM.

C.
A faulty hard drive.

D.
A bad internal USB hub.

Explanation:

Reference:
http://lifehacker.com/5570909/how-to-prevent-your-computer-from-overheating-and-why-itsimportant