Uterly basic checklist:
1 - Check that the computer properly plugged to the wall or a power strip.
2 - If you use a power strip, plug it to the wall. Turn the power strip ON.
3 - Check that the power cord is properly connected to the computer.
4 - Check the fuse of breaker. Change if the fuse is burnt or reset the breaker if triggered.
5 - Only switch on the computer, don't touch the monitor. Last time you turned the computer OFF, you may have left the monitor ON, or turned the monitor OFF and left the computer ON.
Electro, January 2012