Well there is never much help in this section when it comes to the Expedition LLS. More people with LLS knowledge will read it in the Expedition Section.
Now on to your problem. I have to ask the obvious, Have you checked to make sure the switch is in the "ON" position? Sometimes it gets turned off by people, or the accidental wondering foot. If it is on, then lets move on. I did not see that you tested the relay. You can do this by applying 12v to the 2 large wires on the relay. This is much the same as what you did to test the compressor. You can also test the "signal" from the LLS computer to the relay by reading the voltage on the smaller wires. I can not remember off the top of my head what an "OK" reading would be, but I am sure it can be found with a search. I am not sure what else to look at besides that computer. As an FYI, this site http://www.strutmasters.com/
has good prices on parts for the LLS system. They also have many parts they do not list on the site.