We rarely hear about a "broken" reset button, but that is a possibility.
Make sure that the AirPort Extreme is powered up
Hold in the reset button for 9-10 seconds, then release and let the AirPort restart
After a few seconds, you should see the amber light begin to blink quickly. Keep holding the reset button for the full 9-10 seconds
If the amber light does not blink quickly, unfortunately you do have a broken reset button.
If that is the case, it still might be possible to reset the AirPort Extreme back to factory default settings by using the AirPort Utility application. Post back if you need more details about this.