It seems that you want to extend the wifi signal of your root router ?
So you can consider to set it up as a repeater.
The following guide may help you:
http://www.tp-link.com/en/article/?faqid=442
http://www.tp-link.com/en/article/?id=348

I don't want to "extend: the wifi. I ran a Cat5 cable about 130 feet from the Airport Express LAN port to a pole just outside my cabin. I want the TP-Link to connect to my network via the LAN and extend my network across my 150 acres via WiFi (I've also purchased the TP-Link Omni directional antenna TL-ANT2415D).

After trying a few of the different options, I finally just set it up as an Access Point. It works when I connect it to my LAN using a 3 foot Cat5 cable inside the cabin. However, I bought it for outside. I disconnect the 3 foot cable and take it outside to the location where I've run about 130 feet of Cat5 cable. I plug it in and all lights (Power and Wireless Signal Strength) light up except the LAN. I don't believe the Cat5 cable is the problem because I tested it with a line tester and I'm currently running a Foscam FI8905E PoE camera from the same 130 foot Cat5 cable and it works perfectly. However, the TP-Link does not work on it.

Any thoughts on what I can do to troubleshoot this issue?

read this post specially #12 and #13 http://forum.tp-link.com/showthread.php?3320-W5210G-CPE-cabling-scheme&region=china

Am I reading that thread correctly? The Cat5 cable I have installed, which runs other PoE devices just fine, won't work on the TP-Link because it is 'non-branded'? So what brand does it have to be?

can someone provide the recommended cat5 cable so I can run my TP-Link TL-WA5210G with Power over Ethernet?

RedTailHawk you started this post on 01-30-2013 02:54 and posted again 06-11-2013 21:12 so you have not solved your issue, so strange you have not apply your RMA (Return merchandise authorization) TP-LINK has a 2 year guarantee and its clear you have a bad POE, cant buy a new one, they change all the 5210, to get your RMA you have to talk to 01800 from TP-LINK in your country, once you get your RMA number then you take it to your dealer, and takes about 30 days.