Are you using a video card? and if you are what kind? AGP, PCI, PCI E? Or is the video integrated.
Do the following, reseat the ram, the video card (if you have one) power drain the computer, go into safemode , see if it works.
If not most likey the video card or the ram is overheating. Try leaving the computer in BIOS screen for a while if no video signal there or dies out after a while, you got a hardware issue,. if it works in BIOS, then you got a driver or software issue. thanks