I've noticed you can get odd results with the wan port, particularly if you have an odd set-up of ethernet cables. There are ways to even turn on lights for ports that have nothing plugged into them.
Remove all un-needed plugs from your ports except the bare minimum to get your internet back, and troubleshoot from there.
Unfortunately, there are not a lot of options left.
Suggest that you try a Factory Default Reset on the AirPort Extreme to see if that will help.
If you try this a few times, and the WAN port still does not function, it has stopped working.
Repairs are probably not feasible, but you might have a local shop take a look to get an opinion about that.
I know this is out dated. Make sure you check under Internet-> Internet Connections-> Ethernet WAN port. Make sure this is set to automatic. If you have it set to 1000Mbps Full Duplex it can not negotiate with the port if it's the most common 10/100Mbps port. If this is the case it will not know it is connected. A lot of cable modems are 100Mpbs unless they are DOCSYS 3 modems.