It could be a heating problem.

There is a safety feature within the BIOS that will auto shut down a system if the CPU fan quits working or there is a loss of efficiency....dust build up on the heat sink and fan blades, no air flow through case. Unplugged connection to CPU fan and failure of thermal paste between the CPU and heat sink.

A simple test is to open the case and examine the fans when you boot the system to see that they start up ok. With the case open use a small desk fan to blow cool air into the case and see if there is any improvement.