How frustrating this can be, hang in there. When something works one minute and not another, alwasy the simple stuff first, especcially if you have children or animals around your computer. You will be surprised what can come loose after a cat jumps on your desk. Check your physical conections first. Also, check to make certain the power cord isn't pulled out of the monitor, as those cable are ussually a seperate power cord and it can become disco'd.
So, if after you have verified the power is on, and the cable is still connected to the PC, and it still doens't work, then let us know what make and model of your pc, ok? What monitor? What color light is on the monitor when it is "alive", amber or green? Does your pc have an onboard video card? Do you have another monitor to trouble shoot with? Can you get a freind to bring over their monitor to see if their (known good) is acting the same when connected? If it is, then the problem is with the video card, if it works, then you need a new monitor.
Let us know.