Usually it happens when you turn the power saving mode ON. The monitor will go OFF after the specified time say after 10 minutes if the computer is left unused when left over for 10 minutes. Even if you feel the computer does not work while the CPU is running its a good idea to check a few connections are working properly. Try these steps if they appear still the same,
1. First Check with the Monitor whether the light blinks, without turning ON the CPU. This is to check whether the monitor works or not with the light blinking.
2. Turn ON your CPU, check whether the cable is connected with the Monitor properly. Turn ON the screen, shake the mouse, check whether this works else
3. Connect the Monitor with another CPU say your friends computer and check the monitor work good. If the monitor
works fine, then it is in a good condition. If the monitor is not working, the monitor might have a problem with the display. Then its advisable to consult a computer technician.