Chosen Solution
I was normally using the Mac mini with an external HDMI to VGA monitor then suddenly the monitor started showing vertical lines. On a restart it showed Green Apple logo and then permanent white screen without login screen. I have backed up all my data to external USB by booting in User mode so the internal HDD is working properly. I think the graphics card has failed. What are my options other than replacing the logic board?
I believe your diagnosis is correct. Here are the previous responses to this problem: 2011 Mac mini GPU failed (Radeon 6630M) - repair options? I have had some success on the 2011 machine using gfx to turn off the integrated graphic https://gfx.io Manually switch to Integrated Only or Discrete Only mode to force one GPU on or the other.
