How do I fix Apple TV (3rd generation) not opening iTunes Store and failed internet connection test?

Is this for the legacy model A1427 (2012) or A1469 (2013)?

Identify your Apple TV model - Apple Support

Verify that your Apple TV box is properly activated/​registered with a valid Apple Account, by looking up in Settings﹥General﹥About﹥… If not properly activated, it would say “Activation: Failed” there (I think the last line).

Normally, it would take the activation from the Apple Account used during setup. But there might be reasons for that to invalidate (new user, sale, reset, etc.).

User RKG61 offered these steps for stubborn activation a while back: discussions.apple.com/thread/253315520

Access to the iTunes Store (Store services) requires signing in with the Apple Account in Settings﹥iTunes Store﹥…

Access to iCloud services is unfortunately no longer supported on the legacy models.

Apple TV will (try to) connect by ethernet when anything is plugged into the ethernet port.

Only when the ethernet port is empty, then Wi-Fi options should become available.

If the ethernet port is empty and clean and undamaged, and still no Wi-Fi options are presented in Network settings, then this particular unit might be broken for network connectivity as it is supposed to offer.

The IP address 192.168.x.x would be expected when the router is doing DHCP services and leasing out IP numbers to local devices in that subnet. 192.168.0.0 – 192.168.255.255 is probably the most popular subnet for (residential) home networks. The block is reserved as a ‘private’ block for home network use. Both ethernet and Wi-Fi can be in this range; ideally they should share that IP block for the home network.