I've run into this problem more than a few times (Apple TV 3rd generation) whenever I did a software update. Tried resetting router, restart, manual network settings, factory restore, etc., to no avail.
The fix for me was to use bluetooth setup from an iPad or iPhone:
On Apple TV go to Settings -> General -> Reset -> Reset All Settings
After a few minutes, the language choice screen will show up on Apple TV
On iPad/iPhone go to Settings -> Bluetooth and let it discover the Apple TV (for me I had to put my iPhone fairly close to the Apple TV)
Once discovered, you'll be prompted for iTunes username/password and the send diagnostic preference on iPad/iPhone
Wifi settings on iPad/iPhone will automatically be copied over to AppleTV
Once this bluetooth setup is complete everything worked for me again!