AirportExtreme: ethernet ports suddenly not working

Hey all -

In brief, my question is this: Why are the Ethernet ports on my Airport Extreme suddenly not working?

Hardware:

I'm running a refurbished AirPort Extreme (late 2009 model 1354) that I bought from Apple about a year ago. It's run perfectly this entire time until about 2 weeks ago, when the Ethernet ports stopped working with no warning. Wireless networking is unaffected.

Currently, I have a Mac mini (2011) connected to the AEBS via Ethernet (though wireless was usually on too), many WiFi devices, and an XBox 360. I'm running OSX Mountain Lion, though this problem has nothing to do with the software upgrade. I keep my software updated vigilantly. I assume that firmware updates are included in Lion's software upgrades?

Situation:

I came home one evening to discover that my XBox could no longer connect to the internet. It said there was no Ethernet cable connected.

When I turned off WiFi on the Mini, suddenly it couldn't "see" the AEBS or connect to the Internet either.

Steps I've taken:

I've changed out Ethernet cables, so this isn't a cable issue.

I've turned everything off (including the cable modem) for a couple hours, then fired up the modem, factory-reset the AEBS, and started my Mini. After reconfiguring the AEBS, the problem still exists.

Here are my settings for the AEBS currently:

AEBS version 7.6.1

Base station is set up to connect using DHCP. I didn't change any settings on that page.

Configure IPv6 is set to Automatically -- Native

Network mode: "Create a wireless network" -- dual speed networks plus a guest (this is all the same as before it stopped working)

Under Network settings, the Router Mode is set to DHCP and NAT, with no other settings changed

There are no other routers in my house. It's a very simple one-computer, one-XBox network.

I've Googled and read a lot in the forums, but I can't find a thread that matches my situation. Any help you all can offer would be greatly appreciated!

~Lori