I have had this computer for quite awhile, maybe 10 years now. Could it be dying?
The age won't cause it to blue-screen. I've had PCs for longer than that - as they get older you become aware they struggle to keep up (simply because new software tends to assume you're using a newer PC).
If you're getting the screen of death the chances are you've got something corrupted on your system. It could be that your disk is developing bad sectors (which is repairable, assuming it isn't totally trashed), or that a particular file has been corrupted. Sometimes that happens for reasons that never become entirely clear. If you know anyone local who can help look at it they may be able to salvage it, but as soon as you start taking it to the local PC store to recover the chances are it will cost as much as a newer PC.
I asked earlier if it was a laptop or desktop because if the cooling fans get choked with dust (which happens over time) it may overheat and shut down. A couple of years ago a friend had two matching laptops (one for him, one for his wife) and both had major issues. I took them apart - one of them just needed a dust plug removed from the cooling system and the other needed a clean and a new screen. He was expecting to have to drop a grand or more to replace two laptops but in the end it cost him about $50 for a new screen and some beers to thank me for fixing his laptops
(Mark - I put two dollar signs in there and everything in between got formatted funny. I think it's your LaTEX addition, any chance it could be tweaked?)