Chosen Solution
Helping a friend with his iMac (emc2639). It was using Mojave at the time, when it froze, so he did a hard restart. Got the Apple logo, but startup bar would only go half way. I tried all the usual troubleshooting (Disk Warrior, Disk Utility, Drive Genius), all come back saying drive is fine, but I still get the same result (startup bar goes halfway and stalls). Also will not boot into Recovery. He said I could wipe it, so I did (I had to do this with it as a Target drive, because it also won’t boot from my installers). Got it restored back to Sierra, as that its the last one I can do with it as a Target drive. Same problem, get the chime, Apple logo, and then the bar stalls at halfway point. As a Target drive though, it will run my iMac just fine!! When I hold Option key, I see hd with my install, Recovery partition, and my High Sierra install disk, but it won’t boot to any of them. Wah!!
Sadly, you are hitting a failed dedicated GPU. In the older models it was located on a daughter MXM board so it was replaceable! In the newer ‘Thin Series’ it’s soldered directly on the logic board. The reason we can get part way in the POST process as well as run diagnostics is related to the onboard CPU chip graphics engine which is used at the beginning and in both both Diagnostics and Safe modes. Here’s the needed part iMac Intel 27" EMC 2639 GTX 775M GPU Logic Board and here’s the Fixit guide iMac Intel 27" EMC 2639 Logic Board Replacement
