Never mind about the message display, it looks fine now. Perhaps just a temporary thing. (Aside: Is anyone else bothered that after signing in Apple doesn't redirect back to the page from which you signed in?)
After quite some troubleshooting I found if I uninstalled the antivirus (Symantec.cloud, which is basically Norton Internet Security on non-Servers) and turned off Windows Firewall, it still won't connect/sync. I get the same 10 seconds or so of starting, then it disconnects/disappears from iTunes. At that point I am not able to ping the phone.
Further if I ping my phone, my wife's 5s, or our iPad 2 (iOS 7) I usually get "Destination host unreachable" or "Request timed out" until I do something on my phone. Pinging to an old 3GS works every time. So it seems like iOS 7 is either turning off networking when it thinks it is not being used, or perhaps throwing up a firewall of its own until the networking is in use. That may or may not be relevant but in the end if the Symantec software is not installed that's not the problem...the problem would seem to be with iTunes/iOS 7/iPhone 5s.