I had the same problem with the iOS 9.1. Had the 9.2 downloaded and couldn't install it.
Later i was doing something at my iCloud account and when it asked my password, i would get "Verification failed - Error connecting to the apple ID server", or "Try again" the pop-up screen where you put the login and password would just empty the password field making me think I had it wrong.. which it wasn't.. 😠
Looking for answers over the internet I decided to restore it.. but then it was impossible because my Find my iPhone (mine happened with my ipod touch, while iphone 6 and iPad mini are running perfectly) was turned on.. 😟..
My final attempt would then reset everything, so I could restore it, so I started by resetting the "Reset Network Settings" on my ipod touch...
This solved my problem, checked iCloud account and logged in with no problems, activated the Home Sharing at Music and Videos....so.. it was working again.
Hope that helps you guys! I didn't found any mention of the same solution I had over the internet.. .