I have just tried to connect my Samsung Galaxy Tab 3 (8") to a Sky Netgear Router.
In the black bar at the top the WiFi icon has a question mark in it. On the Settings page, in Wi-Fi, it alternates between:
Wi-Fi networks Connecting... SKY00000 Authenticating...
Wi-Fi networks SKY00000 Saved, Secured
I wondered if it could be the router but didn't have time to investigate. I've just arrived at another house with the same router type and I'm seeing the same thing. Neither router had been played with. I'm using my phone to submit this via the router, so it's working fine.
The Tab 3 is new and I'm not at all familiar with Android. Is there anything on it I can tweak?