What is the make and model number of your Spectrum "modem"? We ask because Spectrum does not manufacture modems or routers, so we need to find out exactly what you have that is connected to the AirPort Extreme.
We assume that you have already performed some basic troubleshooting steps as listed below. Would that be correct?
Power off the modem
Power off the AirPort Extreme
Check to make sure that the Ethernet cable from the modem is connected to the "O" port on the AirPort Extreme
Power up the modem and let it run by itself for a full minute
Power up the AirPort Extreme and let it run for a full minute
If you have already tried this a few times, then the AirPort Extreme will need to be reset using a Hard Reset or Factory Default Reset and then set up again from scratch. The reason.......the AirPort Extreme was programmed with settings to work correctly with your "old" modem, but these settings are not likely the same that the new modem will require.
Post back if you need some tips on this, but will still need to know the make and model number of your "modem" to be able to provide the correct instructions.