I had the same issue. Using my iPad mini 2's Apple TV remote and keyboard to enter both ID and password, I repeatedly received the error message, "Your Apple ID or password is incorrect." I also had the same problem trying to sign in to iCloud on Apple TV. Reset and power cycled Apple TV. Power cycled broadband router. Still received the same error message. Simple but unexpected solution: I finally entered the ID and password using the "keyboard" screen on the Apple TV instead of the keyboard on the iPad, laboriously scrolling back and forth through the alphabet and numbers.This input method worked for both the sign-in on iTunes and iCloud. I don't know why one keyboard works while the other doesn't but it solved my problem.