Everything that you are doing is correct.
If you have not yet tried a Factory Default Reset, that might be worth a go.
If still no luck, unfortunately it sounds like the Ethernet LAN <-> switch has failed.
If you have an Apple store in your area, take the Extreme to them so that they can take a look and go over your options with you.
If that is not possible, best to contact Apple support directly.....http://www.apple.com/support/contact/