does it have onboard diagnostics? If it's bluescreening and shutting down, that could be alot of things from OS to RAM to mainboard. diagnostics will rule out a few things, particularly ram and harddrive. You can get third party ram test from microsoft and harddrive tests from major hd manufacturers sites.
Like previous post, OS is also a possibility as I've seen viruses do that to a system. I'd test out the hardware that I could first, HD and memory. If it's not one of those, reload system. If it continues to do that, it's prolly mainboard. Rarely have I seen a processor die but it does happen. Might also be a setting in BIOS.
You say it's refurbed, make sure the memory and processor match the mainboard. No telling what kind of frankenstein box you received. I don't buy refurb for this reason.