I am experiencing this exact problem. I get no video on boot, yet the computer boots successfully and I can access it over the network. I suspect it is related to this big NVIDIA failing GPU issue. There is no fix for it yet, though it's probably going to require replacing the GPU.
I have been able to boot the Mac successfully twice since this problem started occurring. I've been running it now for over 24 hours, and I'm having no issues. If you are able to get it running, make sure you don't restart it or shut it down--it might take you hours to get it working again!