Chosen Solution
I have read lot’s of threads on this site about this problem. I didn’t find the solution to my specific situation. At first this problem was random. Now it’s consistent so I can’t boot up. At first I thought that this was a software issue so I did a clean install of Sierra. Problem: Chime sounds on startupScreen stays black I have tried resetting the PRAM. This seemed to help a few times. Diagnostic leds 1, 2 and 3 (left-to-right) light up on boot. Number 4 doesn’t light up.
Apple may still be covering it: iMac (27-inch): AMD Radeon 6970M Video Card Replacement Program https://support.apple.com/en-us/HT203787
