You are right. This is what I tried first. Again ending in a black screen.
I'd say that could be a graphics driver or EDID problem (or something else entirely). I'd try opening the settings/.../Rearrange your displays dialog and focus the Identify button, then connect the A16. Press space to display large numbers for the connected displays - assuming you get a signal, but the screen is all black, that is. If you have access to a device that can record and playback HDMI EDIDs, I'd use that to make the A16 believe that it's connected to a display and see if that improves the situation.
I think a copy of the EDID of a display will be left in the registry, even after that display is disconnected. You could try decoding that, maybe that helps pinpoint the problem.