Check the picture with light test, inverter is not working if picture is there. Most likely bulging capacitors in inverter section, replace faulty capacitors and fix the problem.

Try to do this: Just before the Windows start up screen (after the bios loading) press F8 and log in at safe mode settings. If at this mode you can see your screen change the resolution settings at a lower set. Save and reboot normally. Now try step by step to increase your resolution. In case of a blank screen appears at a new setting, don't do anything; after some seconds the monitor will come back to the previous settings. Save and go on.

In case of a problem or clarification, don't hesitate to post.

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Stelios