I've got a 2014 Mac mini running OSX 10.11.6 connected to 2 screens; one via the native HDMI and one via a Thunderbolt to HDMI convertor.
It has been running fine for about 2 years. I turned it off around the 19/12/18 and turn it on 7/1/19.
The screen powered via the Thunderbolt to HDMI convertor works fine, and if I swap the screens around I can verify this. But for some reason, the screen plugged into the HDMI port doesn't work. I've done some multi-variable testing to test the various components and can only conclude the HDMI output on the Mac mini isn't working.
I've tried restarting the machine several times and I've tried relaunching Finder several times. But the second display connected to the HDMI port just wont work. It just shows up a black screen with a generic error "check signal". If i go the System Preferences > Display the second display isn't listed.