Hi,
In my case I had the exact same error. I had signed out of my iPad mini 2 a few weeks ago and when I tried to sign in today with my son's ID (I am giving it to him) I got this error. I saw the post about changing networks and I remembered I had blocked the iPad mini 2 in my router settings so it would not be able to go to the Internet at this time; it is only allowed to connect certain times. I lifted the restriction via my router settings and it connected on the next attempt.
I think if you get this, something is preventing you from getting to the Apple servers, because if you do make it, I think you would get something more specific (e.g. ID/password incorrect, etc.).
So in short, make sure you have a good internet connection (if it is too slow it could time out).
Good luck.
.tom