It sounds like when your video card is being pushed, it draws more power than the power supply can supply. This could either be the power supply dying and no longer being able to supply what it should, or some other component drawing more power than it should. I'm not sure how to diagnose that.
It seems like a weird message though, can you screenshot it?
Just in case, download one of those CPU temp monitoring things, and check if your CPU doesn't overheat while rendering.
Video rendering is going to be more GPU based.
Regardless, most random restarts are heat related, so even in the presence of the error message he's getting, dusting out the computer should still be the first thing he tries
