Why is the moniter not powering on

Really need more information here.

Does the monitor not work no matter what device or input you use?

If the monitor does not work no matter what you connect it to, does it show any signs of life? ("Cable disconnected," or "going to sleep" type messages?

If it's completely dead-as-a-doornail the problem is probably on the power side of the equation; bad power outlet in surge suppressor, bad power cable, (It was only once, but I have seen it happen) the LCD power supply itself, or one of the connections in between.

If the monitor works with any other computer on the same input then the problem has to be in the PC.

All the PCs I've ever seen will display a splash screen at an incredibly low resolution that any (working) monitor going back to the late 80's should be capable of displaying it. If the monitor remains in a "Sleep" state no matter what you do to the computer than the issue is sync signal. Either the video card is not generating it, the cable is not transmitting it, or the monitor is not receiving the sync in a way that the chips in the monitor can make sense of.