I am getting the exact same problem. First time I have powered down my router and Apple TV devices since last update and all 5 devices are hanging on the Set Date/Time screen. Can't access any of my Home Sahring iTunes network on Ethernet or get an Internet connection. If I press Menu to drop out of Set Date/Time phase I only have 2 icons instead of the usual YouTube, Netflix etc....what has happened????
There is an Apple support doc which talks about TCP protocols required for AppleTV ( http://support.apple.com/kb/ht2463?viewlocale=en_US ) which says:
"TCP port 123 is used to communicate with a network time server"
I'm just guessing that this might be the root cause, but if it persists it may be worth a call to your service provider to make sure they've not blocked that port. My experience with AT&T (my internet provider) was that they're familiar with requests like this and can open ports while you're on the phone with them.
I had a similar issue with my ATV2. I searched through many different threads on this and other forums and I found a solution that worked for me. Someone suggested to temporarily disable your firewall on your router. Then go back to your ATV and enter your Apple ID and login info. I was able to successfully log into iTunes and set up home sharing with this method. Just remember to re-enable your firewall afterwards.