After completing the 2018-2 Security Update on the Mac mini, I can no longer connect through Screen Sharing. That worked fine before the update. It had to, that's the only way I've used the mini for several years.
I found what I thought was a video cable/adaptor to feed the small, old lcd monitor, but it was actually connected to an Apple audio to VGA adaptor. Apparently, one cannot get Video from the Audio out on the mini.
Naturally, I can't find an HDMI to VGA anything in the house. I may have never actually connected
any monitor to this mini! If I did, I have no idea why I would have thrown away the adaptor.
At any rate, I suspect that if the video card is dead you can't use Screen Sharing either. At least I can still see, edit, swap files through Finder/Pathfinder.