The AirPort Extreme will not "show up" in AirPort Utility after it has been Hard Reset, so that might help explain some of the difficulty that you have having.
After a Hard Reset, the AirPort Extreme is now back to its factory default settings, so you will need to set it up again using the instructions provided in the Setup Guide that came with the AirPort Extreme.
Assuming that the Hard Reset has been performed correctly......meaning that the Extreme has been powered on for few minutes and you have held in the reset button for 7 to 8 seconds, then released and waited a full minute for the Extreme to restart....
The next step would be to click on the WiFi icon at the top of your Mac's screen and look for a listing of New AirPort Base Station. Just below that heading, click directly on AirPort Extreme.

When you click on AirPort Extreme, that will get the setup "wizard" up and running. It will take a few seconds to analyze the network then display a screen that looks similar to this:

Follow the prompts to set up the AirPort Extreme again.