Connectivity issues on touch 5th Gen...

Hi, My 5th Gen touch is exhibiting weird behaviour! It won't connect to iCloud at all.

When I try to enter my credentials in Settings > icloud I get the message "Verification Failed. There was an error connecting to iCloud". (I am entering correct login information, and have verified by connecting from PC)

If I try to create a new Apple ID from Settings > iCloud, I get the message "Cannot create Apple ID. Unable to connect to server".

If I go to Settings > General > Software Update, it won't check for an update as it says "You are not connected to the internet" (I am, and can browse websites etc, as below).

If I browse the internet from the device, I can get to places like Google.com, bbc.co.uk etc, but can't get to GMail, yahoomail etc.

It's almost as if there is an issue connecting to secure (TLS) addresses?

Things I've tried after reading the forums:

* Settings > General > Reset Network settings

* Settings > Date and Time > Automatic time Zone

* Put the iPod into recovery mode and completely restore it to factory defaults with latest iOS (8.4.1)

* Tried it at various different houses and at work to remove the possibility of WiFi router issues...

Does anyone have ANY idea what might be going on??