Apple TV - Can't Sign In, or use YouTube (but other stuff works)
This may sound weird, but, unplug the Ethernet and connect to your wireless network. You should have access to all internet services. Some thing happened with my ATV out of the box, but using wifi solved the issues. Apparently a bug with that version of iOS. Apparently they fixed it on the latest update but I never went back to Ethernet to test and it's been fine on wifi.

It's something to do with the relay back to Apple servers apparently, but seemed like a weird bug.