It sounds like a hardware error to me personally. Does your mobo look good if you open the case? Are the capacitors or anything corroded by any chance? Always a good idea just to check it out physically and see if there's anything possibly conflicting inside her.
I would try to run diagnostics on the machine. Test out everything, scan your HD disk for bad sectors possibly and surface damage using a DOS prompt or something of that nature. It could be video...but probably not. Your system sounds to support it, plus Civ4 should be okay with a 7series vid card.
Something could be dying though. PSU could be losing power or dying off, if it takes a while to power on that's not a good sign. Make sure the fan(s) are running in that thing also, if they're not, it's dead and get a new one. Also could be a motherboard issue as well.
It sounds like hardware to me, try to get your hands on some hardware diagnostic tools if possible. Also check out this site at www.pcpitstop.com
and go to full tests option at top left. It will test your machine and maybe pick up some issues with hardware/software that you didn't know about. I love that site.