Is this a power supply issue or video card problem?

My computer is running great. The problem i have now is all of a sudden my computer monitor goes dead as if it has lost power. my computer still has power. The strange thing is I unplug computer from ac power and let it sit for a few minutes. I then reconnect and computer works. This shut down does not have any time frame. It can run for hours with no problems,then sometimes after 30 minutes I get this shut down. When the shut down happens my case is still getting power. The case fans,the fan on video card,fan over processor card all still running. restarting computer doesn't help. The only thing that gets the computer running again is to unplug power supply let sit for a few minutes. Is this a power supply problem|||Give me your computer specs, if you dont have a PSU with enough wattage then it could be the problem, what I'm confused about is whether you have a desktop or a laptop, i guess you have a laptop if your monitor is running off the computer power supply...im very confused about your setup, more info please!!