Hi Everyone...
I have a 24" Cinema display and have been experiencing similar issues as described above. Two years ago I took the screen to a repair facility and they told me it was the logic board that was not working properly. The repair would have cost around $300 dollars... it was just not worth it. I took the screen home with the intention of recycling it but never got to it. The screen stood around 2 years not being connected to power supply. Today I thought I would get rid of it but before I did so I wanted to try turning it on one more time... Connecting it while macOS is running the same problem persists. Screen flickers for half a second (I see my desktop image) and then goes black. Unplugging and re-plugging did not help either. I wanted to try one more thing though and that was seeing if there is any change when my macbook pro is running Windows via bootcamp... And alas! Starting windows, the screen not only flickers for a millisecond but for about 5 seconds and then turns on completely normal... I am writing this connected to the screen and it works fine. I have not rebooted through macOS yet but will try that today. Would be interesting to see if some of you are having the same findings.
Nick