How do I resurrect a Thunderbolt display?
I have had a similar issue a few weeks ago. In my case the screen was not "completely" black, but it was close. Going to the "Display" tab in the settings app and turning up the brightness did the trick.

However, it may also be an actual hardware failure if there is nothing at all visible on the screen. In that case you should take the display to an Authorized Apple Service center.

In the pulldown, select Mac repair since these require the same training, tools and skill to repair as an iMac does.