I'd check the power supply on it... because it is new. As well as the power supply switch (it could be faulty.)

Further I'd run a memory test to see if memory could be responsible for the shutdown trouble.

http://www.memtest86.com/


But before that you might want to run a scan for spyware, adware, viruses, etc...

http://www.techzonez.com/forums/showthread.php?t=9739