Thanks, but you provided the model number of your Apple AirPort Extreme wireless router......not a modem. Unless your AirPort Extreme connects directly to a wall Ethernet port, you have a modem or gateway there as well.....a device likely provided by your Internet Service Provider.
If you have a simple modem, it will look something like this on the back panel:
If you have a modem/router, which is also called a gateway, the device will look something like this:
Until we know more about what modem or modem/router you might have, we are kind of stuck.....since there are some settings that will need to be checked on the AirPort Extreme to make sure that they are correct. These settings will vary depending on the type of modem that you have.
So, as we said, we're kind of stuck at this point, until we know more about how your Internet signal reaches the AirPort Extreme.
Connecting a computer directly to a modem is a basic troubleshooting step that determines whether the modem is working correctly or not. If you are not able to connect a computer directly to the modem to test that way, we are not sure how else to test to make sure that the modem is operating correctly. We are very surprised that your provider did not ask you to do this when you were working with them.