If you can't ping the other devices from each other, you've definitely got a "network problem" as the Denon puts it.
As to the DNS, if you've only got one, just put it in the primary field. Proxy should definitely be set to off.
If you put a router after the att modem, you'd want to put all of your devices behind it so as to keep them on the same network. Part of the issue is that the att modem is already doing NAT (translating your outside ip address into multiple inside ip addresses) and because it's pretty generic to use 192.168.1.x, your existing router probably also uses that. It's a no-no to use the same network on both sides of the router, so that would undoubtedly break everything.
