Computer...Dying?

[abracanabra]

The last couple of days, my computer's added a new and very not good quirk--blacking out the screen. I'll power up, be using it for a couple of minutes, and *poof* black screen. The computer itself is still running, there's just no display. If I put the computer into sleep mode and bring it back up, the screen displays again--for a while.

Help?

Is this a monitor problem, a graphics card problem, a virus--what? What should I try to do?