Without more infomation, I can't give any detailed insights on your problem. I can give some general advice, though.
1) Power leads. Make sure that both computer and monitor have working power leads, connected properly. Even the most experianced people screw this up sometimes.
2) Problem with the connection between computer and monitor. When you turn your PC and monitor on, if your monitor does not kick in, it could be that it is not being sent any visuals to display. Check the lead between the monitor and PC is in good condition, and is plugged in the correct slots. If there appears to be more than one place to put the lead into on the computer, try one at a time. If this soes not work, there may be a problem with your computer itself. If you can, find another monitor (even a small old one). Connect the old monitor up, and test. If the old monitor also is blank, there means there is a problem with the computer itself, not the monitor(s). Then I don't know what to do.