It "should" work flawlessly without having to mess with it too much.
reset it back to factory defaults, power down your computer, power down the Extreme and the modem.
Bring it all back up again in the reverse order. Modem, Extreme, computer. Wait until each one is ready before moving on to the next.
Once up, configure the Extreme using DHCP.
I bought an AirPort Extreme Wireless-N this weekend and hooked it up to my cable modem at home. I used the Airport Utility to set up the base station and create a wireless network. At first I used DHCP to set up but got an a yellow light and a message saying that the internet connection was not working. So I hook my MacBookPro directly to the cable modem ethernet port and got all the IP Address, Subnet Mask, Router and DNS information from my ISP, Cox Cables. I then connect the AE to the cable modem ethernet port and used the Airport Utility to set up the base station again. I chose manually set up this time with the IP address I got from ISP. I got it working without any problem and my MacBookPro was able to detect to the AE. However, I still can't access the internet. The light on the AE itself is solid green, but there is no connectivity to the internet. I'm at a wits end as to what to do next. Any help will be appreciated. I'm using Mac OSX v10.6.6.