[Coda]

The power supply isn't a battery at all. The only battery in a desktop is the little button cell that keeps a tiny amount of memory saved while the power is off. But yes, when a power supply goes out you can usually just replace it. It's not likely that the motherboard would have taken too bad of damage from it failing that way -- it would be another matter if it blew out from a lightning strike or something, but you should be okay here.

Just make sure you buy one with at least the same wattage, and don't get the cheap ones because they can't sustain their rated load and burn out more often. If you're paying $50-$70 you're probably okay.