If you are having network connecting issues with your Apple TV, you may find the following article helpful:
I had this problem and found an interesting solution:
My Apple TV wouldn't connect, but only gave the error message prompting me to connect to home sharing. Then it asks to login with Apple ID, but it wouldn't recognize my ID and password (even though I entered it correctly). I tried to authorize the Apple TV from iTunes on my computer, but this didn't make a difference. It turns out the problem was in the Ethernet / Ethernet-Wifi adapter connection, and instead of changing the connection settings, I had to unplug the Ethernet, and then search for and connect to a Wifi network.
My lesson is, if the Apple TV gives you an error message, it may be incorrect, so make sure your device is connected properly to a network.