Go through the following points until the problem is resolved:
Check the power button is switched on.
Check for any power indicators on your monitor – are there any lights on?
Check the monitor isn’t in standby mode.
External power. Check the power socket – is it turned on and working? Check another socket that you know is working to see if this makes any difference. If you’re using a multi-way extension plug, try connecting directly into the wall socket.
Cables (1). Follow the power cable from the plug socket to the monitor and to the computer. Are all the connections secure? – feel the connections and push them in to make sure they are tightly secured.
Cables (2). If your plug socket is working, and all the cable sections are tightly secured, you could have a problem with the connecting cable. Replace the cable with a cable that you know works.
Some monitors also have a secondary switch to cut the power completely – check if yours has one, and if it’s turned on.
If you have checked all of the above and your monitor is still not responding, then you could have a problem with your monitor. This could be for a number of reasons, and you will need to get the problem checked out professionally.