In the last few weeks have had half a dozen Chromebooks sent to me for repair with a black screen issue. Indeed, when you pressed the power button you could tell that the screen was getting power, but you just saw a black screen and nothing else.
The good news is this was an easy fix. Basically the Chromebook needed a forced reboot. To force reboot a Chromebook press the Power button and the Reload button.
This forces the Chromebook to reboot. Remember the old PC reset buttons?
This may or may not fix your issue, but it’s definitely worth adding to your bag of troubleshooting tricks.