OK, thanks for the additional information. Please follow the instructions below carefully.
Power off the modem completely by turning it off and then pull the power cord from the back of the modem or pull the power supply from the from the wall AC jack.
Leave the modem powered off for at least 30 minutes. Longer will not hurt at all.
During the time that the modem is powered off.....
Power up the AirPort Extreme and let it run for a few minutes.....if it is not already on
Hold in the reset button on the back of the AirPort Extreme for 7-8 seconds and release. The reset button is located next to the power cord jack.
Allow a full minute for the AirPort Extreme to restart to a slow blinking amber light status
Power off the AirPort Extreme by pulling the power cord from the back of the device or pulling the power cord from the wall AC jack
After the modem has been powered off for at least 30 minutes......
Connect the Ethernet cable from the modem to the WAN "O" port on the AirPort Extreme
Power up the modem and let it run by itself for 4-5 minutes
Power up the AirPort Extreme and let it run a few minutes
Click on the WiFi menu at the top of the Mac's screen and look for a listing of New AirPort Base Station.
Just under that listing, click directly on AirPort Extreme
When you click on AirPort Extreme, that will start up the AirPort Utility setup "wizard"
Follow the prompts to set up the AirPort Extreme again.
You can use the same device name, wireless network name and password that you used before, or you can set up new names and passwords.
Assuming that the new AirPort Extreme is functioning correctly, your network will be functioning correctly now as well.