If the firmware required an update, and that was not applied,
a problem may exist where a cure could have fixed it...
Identification of the model, so as to apply the correct item
is important; since the incorrect one won't fix an issue in
hardware it was not intended to resolve.
•Mac mini EFI Firmware Update 1.6 - for 2011 MINI
helps issue with USB ports and connectivity
•Mac mini EFI Firmware Update 1.7 - for 2012 MINI
helps issue with HDMI issue, not said to be for 2011.
There may be a hardware issue, so if the unit is correctly
identified as a 2011 model, the firmware update may not
help, as it is Not said to address that specific issue. So,
you may need to inquire of an Apple Authorized service
or ask an Apple Store with Genius bar about the unit, it
may (or may not) be something they could help you with.
You could try & see if this reset (try more than once) could
help the issue; it may be a hardware failure. Check all the
cables, plugs, and ports to see if the issue is not in Mini.
•Intel-based Macs: Resetting the System Management Controller (SMC) - Apple Support
Perhaps a genius could perform a stress test on video
or see if some other items appear weak in a test. If a
genius in official Apple Store location is unavailable, you
may have to locate an authorized service provider who
has staff with experience troubleshooting Mini graphics.
A problem may indicate a repair, if SMC reset, or other
hardware (cable, display, other cause) doesn't fix it.
Did you try the SMC reset to see if the system power
management controller may affect this situation?
If you are sure (by serial number lookup or records) the
computer is a Mid 2011 build, not a Late 2012, the first
and earlier EFI firmware update may have been applied
already. Correct identification helps in such matters...
•PS: Do the web page URLs in your post have significance?
Good luck & happy computing! 🙂
edited