mcs- it could possibly be, but unlikely cause its a fairly new machine, bad cpu goop.. I know on older machines the goop that goes on the CPU under the heatsink tends to dry out, and your cpu will tend to overhead, causing random shut offs. Also same thing with the video card. It could be a number of problems, but being about a year old, I would call and see if you are covered by warranty. Like a few others said, be careful on repair costs, computers these days are getting really cheap, and its not worth spending a few hundred $$ in most cases to repair one. If it is your only option finically though, then it is the path to go. I am sure between all of us here, we can help you figure out your problem. I won't charge to take a look at your computers, as I am already indebited to miles city for all their support for me.
Good luck and keep us posted