The airport extreme is already connected by ethernet cable to the google modem.
Please review the post by LaPastenague again to confirm that he was suggesting that you connect your Mac to the AirPort Extreme using an Ethernet cable to set things up again.
If the computer and the airport extreme are far apart just disconnect the Extreme from the network and plug it into the iMac by ethernet.
The weblink discusses airport express, but I have airport extreme
The manual setup is the same, no matter whether you have an AirPort Express, AirPort Extreme or AirPort Time Capsule.
Also, I was hoping that I would not have to do full factory reset
Since you cannot access the settings of the AirPort Extreme to check them using AirPort Utility, there is really not much else that you can do other than reset the AirPort back to factory default settings and then set it up again. If you call Apple Support, this is usually the very first thing that they advise.
Here, I assume that you have already tried powering off the AirPort a few times and restarting your Mac. If you have already tried these things a few times, it is time to reset the AirPort Extreme and start over again with a new setup.
If you do not want to use the manual setup procedure that LaPastenague suggested, post back for a few tips on using Apple's setup "wizard" to handle most of the setup quickly and easily.