The outboard power supply for an A1408 AirPort Extreme....some folks call this type of power supply a "brick".....looks like the device in the link above...and below again...that I provided.
http://www.ebay.com/itm/ORIGINAL-OEM-APPLE-AIRPORT-EXTREME-BASE-STATION-POWER-SU PPLY-AC-ADAPTER-A1202-/370810566512
It's possible that the Apple Store might have one of these on hand for sale, but it's also likely that it will cost twice as much as the replacement that you can order. If the AirPort Extreme works when the Apple Store tests with another power supply, that at least let's you know where the issue is.
If the test with another power supply does not work, there is not really much that you can do. If you happen to have AppleCare in effect on one of your Macs......AND.....the AirPort Extreme is less than 3 years old, Apple will arrange for you to receive a replacement at no charge.