Will not cme on
Firstly - Is the cabling, mains and data cable, securely attached at both ends and the power turned on at the mains?
Secondly - If so when you press the monitor power button, does a light come on? (often orange coloured) If yes does this change colour when the computer starts its boot sequence? (often to green or blue)?
If no light can be obtained it is likely that the monitor is faulty.
If a light comes up on power up, but doesn't change colour during the computer boot sequence then it is more likely to be the graphics card that is faulty, or sometimes the computer PSU.
The easiest way to find out whether the computer or monitor is at fault is to replace the existing monitor with a monitor that is known to be in full working order, for example from another computer. (Or connecting your monitor to a computer that is known to be working)
Having isolated the faulty component it can be replaced and you should be up and running again.
Hope this is helpful, if so would you please register that with Fixya