So recently a new problem has arisen.....basically, while rendering an image, my computer just turns itself off and then turns itself back on.  At first I though this was due to my monitor, which, around the same time, began to fade and change color.  But now I have a new monitor and the problem pursists.  Also, at first I thought it only happened when I rendered with Premium, but alas it seems to happen all the time now.

Has anyone ever had this problem....any suggestions?

The one time I had a machine shutting off on it's own was from overheating.
Are your fans working?
Are your air vents clean?
The second one was what was happening to me. The back vents were clogged and not getting any air circulation.

Yeah that'll be it, overheating for sure. If your motherboard has a temperature utility that can display the temp in a little icon in your tray, maybe then you can see when it starts to get too hot.
As dvlenk6 suggests, could be a fan problem or dust, so it looks like you'll have to take the side of your case and check it out.
Best of luck with that.

Yup I agree.  Check for over heating.  Most important you're CPU Fan make sure its working and also free of dust.  As dust acts like a blanket and keeps things nice and toasty which is a    no no.

Overheating.  Get a water cooling system besides the fans.

I'd say probably overheating. Check if all fans are clean and defenitely dont forget the cooling element on your cpu. Dust can sometimes really pack up in there.
If neccesary, use some toothpick or such to scrape densely clogged dust out between the ribs of your cpu cooling element.
Always be nicely carefull though because there's fragile hardware in your computer.
Watercooling is nice, but if it leaks ur screwed and unless you plan on overclocking your computer its kind of overkill.

A warning about water cooling......

http://www.avforums.com/frame.html?http://www.avforums.com/forums/showthread.php?threadid=56924