Graphics card issue??

I need help i just got my new computer and at random times my screen starts to stutter shut off and sometimes even making my computer restart. Is this because of the graphics card??

Specs

Phenom II X4 965

ATI radeon 5870

4 gb ram

1 tb hdd

700W PSU

What make an model PSU do you have? Just being a 700-watt doesn't tell the whole story.