Probably worth trying a full factory reset.
Originally Posted By: Apple
If the AirPort Base Station or Time Capsule isn't accessible from AirPort Utility, the Factory Default reset can be accomplished by using the reset button.
  • Unplug the AirPort Base Station or Time Capsule from power.
  • Press and hold the reset button with a pen or pencil, then plug the AirPort Base Station or Time Capsule back in while continuing to hold the button until you see the light (LED) flash rapidly. This should happen after a few seconds.
  • Release the button. This will factory default reset the AirPort Base Station or Time Capsule.

Had to do this on one of my older units, and it brought it back to life. If this doesn't work, any valid Applecare agreement on a Mac in the household will cover Airports too.