What is AirPort Utility telling you when you plug it into one of the Ethernet station ports? If you can see the AirPort it should be giving you some red error markers most likely the Router can't find the upstream gateway to resolve the path.
Next try plugging in two systems into the Ethernet station ports can you get them to see each other? The hub part of the AirPort should still be working only the Router part to the upstream port and WiFi likely not working. Not much you can do here time for a new unit.