If caused by malware, it is often possible to start the machine in Safe mode and run anti-virus/spy-ware utilities, and HijackThis to locate and remove/correct the problem. It can also be helpful to try a different monitor as well as learn how to work in the dark i.e. learn the keyboard commands for running the anti virus and anti spyware utilities as well as System Restore.
See http://support.microsoft.com/kb/126449


For keyboard shortcuts regarding particular programs contact their Support team or forums. Or see http://www.geocities.com/~budallen/hotkeys.html#Make%20Your%20own

Also, a completely dead monitor is often indicative of loose or unplugged cables.