Hardware troubleshooting through process of elimination. Unplug the video cable from the monitor and power it on. It should show "No signal detected" or something similar. This is basically the built in test on the monitor, if you see the a message the monitor is probably fine.
LAPTOP Unplug the power and remove the battery and hold the power button down for about 10 seconds. Plug the battery and power back in and test.
DESKTOP Unplug the power and hold the power button for 10 seconds and plug back in and test
If you still get nothing let us know if this is a laptop or desktop to troubleshoot further.
If just a light flashes then it may mean that this is a Motherboard issue. Do you get any Beep code with this problem? What is the make and model of your system? These things would help us better understand this problem.