Why does AirPort Extreme say it has no internet connection (flashing amber) but the wired Ethernet connection works fine?

I just picked up an AirPort Extreme, expecting a relatively painless setup, but I can't seem to get past the flashing amber. The AirPort Utility shows amber next to Internet Connection and 'No DNS Servers' and no IP address or LAN IP address, but the Internet is shown as green and my iMac connected to the Ethernet port of the AirPort can access the internet just fine.

Any tips?