I have a mac mini 2011 the one with the dedicated AMD graphics card. I've tried twice to update to the latest sierra update 10.12.4 and it stays stuck at the grey screen with apple logo with about 80% of the progress bar filled, after the upgrade. After waiting 4 hours i tried to trouble shoot but in the end i had to reinstall from the recovery drive and a time machine backup.
In short, both attempts resulted in the same problem, however contrary to OP i was able to see my screen. After restoring from time machine backup i am sticking with 10.12.3 until this is fixed, which might take a while. Apple tends to ignore this machine a little bit. I had an issue in the past with an update that broke the HDMI drivers for my specific Mac Mini (the only intel mac mini that ever had a dedicated graphics card), and it took apple a while and some convincing before they fixed it. Myself and other owners of the same model mac mini were filing bug reports.
If you have a backup i would suggest you try to restore like i did. Hold option when booting up and see if you can see the screen and select your recovery drive.