How long have you been running Windows 8? Perhaps your computer isn't up to snuff to run it.. Also if its a preview build, its not 100% stable.
Finding out what power supply you have involves opening the case and looking at it, I'm going to guess its a cheap crappy one. Can't guarantee that is the problem though. The best way is to swap in a known good power supply into the system and see if the problem continues. How often does it lose power? Have you tried another outlet in your home? I know that sounds silly, but you'd be surprised how often that happens.
I'd still suggest installing a stable operating system, sounds like an awful old machine to be running Win8.