Could be any number of problems, from something as simple as your computer putting the monitor into standby, to incorrect graphics settings, to electrical/mechanical issues. Does its LED or light on power button indicate that it is actually on?
The only LCD monitor I have ever seen fail was a Dell 17". I am not sure what the problem was, but I suspect that it was a bad solder joint for it VGA connector. Normally the power button was green when on, or blinking amber in standby. At first when it would not wake up from standby, moving the VGA cable would wake it up. But eventually when it would not wake at all, the power button was blinking green, which was unusual and apparently some sort of error. The same computer and cable has worked fine for another monitor since then.
If you have a separate video card, it could be that the contacts got corroded and removing and reseating the video card may help. Or maybe connectors are not fully seated. When I first connected a BluRay player to the HDTV I use as a monitor at home, I got the player menus, then nothing. The HDMI cable in back of the BluRay player was not inserted far enough, and had come loose.