I'm not a networking expert, but it seems that the problem is that the phone is not connecting to any DNS servers. This is not something that the router handles. This is evidenced by the fact that if you try bypassing a DNS server, you can access the webpage you're looking for.
Normally, when you type in a URL, the system sends a request to a DNS server, which has the information about what IP that URL name is attached to. It seems that this connection is what is broken on our Pros.
For example, I have a site f4dlighting.com. If I type that into the browser, it tells me the webpage is unavailable. Clearly, since I run this website and have a computer where the internet does work, I know this webpage is, in fact, available (regardless of the fact that I only have a basic index page up at the moment). However, I can type in the IP address of my website, (208.43.212.208/~fdlighti/), and it pulls up the index page just fine. I've tried this with a second site that I run, as well as a couple of other sites that I found the IP addresses of.
So yeah, basically, it seems that some file in the phone is either prohibiting the connection to a DNS server (possibly corrupted or something), or a file that is needed for the connection is missing.