DisplayPort problem? Hopefully you have a DP-to-DP (or miniDP-to-DP) cable, no adapters, no converters, no extenders.
Disconnect any USB devices on the monitor until it works.
Are you sure your graphics card is outputting a signal? A recent NVidia update apparently "fixed" some DP issues, if that helps. It doesn't hurt to reinstall DirectX and AMD/NVidia drivers, at least it will return to default display settings.
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