iMac 5K, 10.11.3, Apple TV 2, Software 6.2.1
I have no problems using Apple TV from my iPad or my MacBook Air (Yosemite 10.10.5) but it does not work with my iMac. Sound but no display.
I made sure the firewall does not block any communication but whatever I tried - no picture. I also tried Safari iso Chrome, same thing.