Oh man, you are in luck. The rusting point is right below the driver's seat (at least on mine) and the precedure should not take you more than a few hours, maybe a day, hehe. Anyway, start by removing the driver's seat (2 bolts and 2 nuts), get it out of there and watch out for the seat belt. I have read somewhere that there is something that will engage the seat belt locking mechanism and a new seatbelt will be needed, well, it is not so on mine, but I would advise to check online for some seat removing precedures before you go on.
After the seat is out, I would think that the easiest way to get the carpet high enough for you to access the points of connection is to remove that plastic piece the carpet goes under and the door goes on top of, basically you just yank that piece up (you can look for some DIYs on this too, easier with pictures), then you would probably have to do the same for the one by the rear door and most probably get that plastic piece between the doors a little bit out on the buttom (be carefull with this one, the plastic clips break VERY easily). Try to raise the carpet after you do each step because you might not have to get all of those pieces out. Try removing the front plastic piece first, than the middle and then the rear if you don't get enough clearance.
Now, to make it easier for you to go on I will try to explain where the damn thing is. It is a flat, wide piece of plastic with I think 5 wires going to it, it is located on the front side of the brace the driver's seat mounts to, so basically, the nuts you had to unscrew to get the seat out, sit on the screws that are right on top of that brace. Get a flash light and try to find that plastic piece, I think it is right by the door. If you see it all rusted inside, just yank all the wires out and connect them together with a wire nut or something similar.
If everything went how I described, your locks should be working perfectly fine, if that thing was not rusted or anything similar, well, all I can say is sorry and that is not the problem. My mechanic took apart the doors and half of the dashboard to try to figure everything out and he said the signal was sent but was lost somewhere along the line. Good luck with that and tell us how it went.
cladge, I am not a mechanic by any means and don't know much about anything but if I was in your position I would get the brain of the system checked out, or maybe you just have a dead battery in the remote. Try calling the dealer and getting some info out of him, maybe there was a recall or maybe it is a common problem. Other than that I can only reccomend either going to a mechanic or replacing one piece after another starting with the cheapest. Good luck to you too and tell us how if you found the problem.