I have a similar issue with my wife's 2012 17" Retina display. The computer boots up. Using Screen Sharing, I get a display that is almost square, like one would get with a headless Mac mini, rather than a display window proportional to 2880 x 1800. In addition, it does not recognize any external monitors. Occasionally when trying to reset SMC and/or PRAM, I can get the display to work for a few minutes, but then it goes black again. I've tried disconnecting the battery, removing the solid state drive (and booting off an external drive), and other standard trouble-shooting tips, but to no avail. I reinstalled the latest compatible OS (10.13.6), but the issue persists. I did manage to do an extended hardware check once when I had the display working, but it gave no hints of any problems. I am at a loss.
One odd thing: the battery had been giving a warning indicating need for service/replacement. After fiddling with it, it now says it is "Normal". But I also get the problem with the battery disconnected.
Any ideas?