Airport is does not have an IP address and cannot connect to the internet

I would recommend that you do the following as a minimum:

1. Power-down the modem, AirPort base station, and computer(s).
2. Power-up the modem; wait at least 10-15 minutes to allow it adequate time to initialize.
3. Power-up the AirPort base station; wait at least 5-10 minutes. Note: The AirPort's status light may continue to flash amber after it has intialized. That is because, there may be some additional configuration items necessary, like setting up wireless security, before the overall setup is completed to get a green status.
4. Power-up your computer(s).

If the above steps do not solve the problem, start over with step 1 above, but then perform the next steps between steps 1 & 2. above.

1. Disconnect the AirPort base station from the Internet broadband modem.
2. While all of the devices are powered-down, perform a "factory default" reset on the base station. This will get it back to its "out-of-the-box" configuration and make setting it up much easier, especially if you use the "Assist me" process within the AirPort Utility. (ref: Resetting an AirPort Base Station or Time Capsule)
3. After the base station resets, go ahead and power it back down.
4. Reconnect the AirPort base station to the Internet broadband modem. For the Extreme and Time Capsule, be sure to connect the cable to the base station's WAN (circle-of-dots) port.
5. Continue with step 2 in the first set of steps.

In this basic configuration, the AirPort base station will broadcast an unsecured wireless network with a Network Name (SSID) of Apple Network NNNNNN. Network clients, connected to the base station either by wire or wireless, should now be able to access the Internet through the ISP's modem. Once Internet connectivity has been verified, you can use the AirPort Utility to configure the base station for wireless security and any other desired options. Please post back your results.