I have experienced exactly the same thing.
It is definitely the driver, because I've tried everything from, reinstalling Windows 10 on a separate disk, switching out PSUs, reseating the GPU in the PCI slot and trying the card in a different computer. All attempted solutions result in the same black screen, no display output.
There is display output during POST and when booting in safe mode as well as booting into a Linux distro, but that's simply because the drivers for the 6900xt aren't signed and loaded at those times. It is only after reinstalling the driver and Adrenalin software during and after performing a DDU in safe mode, do I experience the totally blacks out display/no display issues. Exactly when the message bar in the software installation reads, "screen may flicker and go blank".
The only problem is, the screen does flicker, go blank and never returns. Even after a reboot.
I have read where others have been experiencing this with the 6800xt, too, yet with older drivers.
PS: I got this card 2 days ago and it ran well until I was playing Batman Arkham Knight and saw a lot of graphical debris and artifacting, after a few hours of gameplay. I tested other games and the same debris, artifacting and distortions occurred. I thought it might have been my HDMI cord, but that turned out to not be the case.
Something is definitely wrong with this driver release and something needs to be done about it, asap. Nonetheless, any and all recommendations are welcome in rectifying my issue.
I hope AMD has a solution for this, because I'm about to RMA.