Is any power getting through to the monitor? Do you have a different power cable to try? Or another computer you can connect the monitor to? Lastly, does your Mac or the monitor itself have AppleCare?
If you can't troubleshoot it yourself, book a Genius Bar appointment at the nearest Apple Store (if one is available in your area). Hopefully your monitor is still covered and they can help you diagnose the problem and repair/replace the monitor.