Tim,
The way I have the routers connected is secondary to my problem, I think.
Every other device in my network from Andoid phones to an iPad all get IP addresses and connect over WiFi and my Desktop connects via ethernet.
The Arduino board is the only one that doesn't work. I'm thinking it's bad. It's one of those third party boards from ebay (US seller kbellenterprises) with the HanRun ethernet jack. I don't know if anyone has had these issues with them, but I certainly am.