You may not be aware that it often takes 30 minutes or more for a cable modem to completely reset....despite what your ISP might tell you.
Otherwise, the modem stays "associated" to the previous device and will not "recognize" and issue a new valid IP address.....likely the exact problem that you are experiencing.
Power off the modem by pulling the power cable from the back of the device or from the wall AC jack
Pull the internal battery on the modem if it is easily accessible
Power off everything else on the network
Wait at least 30 minutes....longer will not hurt at all. Some ISPs take up to 2 hours to fully reset the connection.
After the wait period, reinstall the modem battery if it was pulled previously.
Power up the modem and let it run for 5 minutes by itself
Power up the AirPort Extreme and let it run for 5 minutes
Power up each network device one at a time about a minute apart
Check the network
If you are still having issues, it will be necessary to perform a Hard Reset on the AirPort Extreme by holding the reset button in for 9-10 seconds and then letting the AirPort restart.
Then, repeat the entire process again.