I've found out it is an Mavericks 10.9.2 and 10.9.3 failure! Online I have found more people with the very same Problem, and all of them are running 10.9.2/3 - ON THEIR IMACS (different Models)!
My Apple TV and Streaming Services were functioning just fine 2-3 Monts ago, the only thing that changed was Updating my iMac Mid 2011 to 10.9.2 -> Then i've got the black screen when streaming, could not activate DisplayMirroring, when i played something in itunes or VLC the sound went through AppleTV but no video.
Then have checked it with iPad 2 = OK, iPhone 5 = OK, MBP Early 2008 with SnowLeopard = OK,
so i decided to Install an 10.9 on an external drive - and guess what? It works! Tried to Update (ComboUpdate) to 10.9.1 and it was still OK, got the BLACK SCREEN after ComboUpdate 10.9.2, and tried to Install 10.9.3 just to see if it will solve the problem -> NOT
this must be a joke!