DEI Rattler 369d Remote?

Hi, I have a 2004 Ford Expedition with a Rattler 369d remote start/keyless entry system installed. When I first bought the vehicle it had a remote for the system & it seemed to work when I tested it. However, the battery in the remote died promptly after getting the vehicle home. I proceeded to open up the remote to replace the battery, but in internal components of the remote fell apart as it was terribly corroded inside from what looked like the remote being dropped in a puddle. I set the remote aside in hopes of replacing but it has since been "misplaced" (which is code for my wife most likely tossed it in the trash...lol). I've tried looking for the correct remote but after purchasing not one but two different types, neither have worked. I can't remember the 1st remote model I tried, but the model I have right now that isn't working is a DEI 474t. I can get the unit in the vehicle to enter programming mode (light on unit blinks appropriately but no horn) but it is not recognizing the remote when I attempt to program it. I'm assuming that I do not have the correct remote model? If so, could someone please tell me which model remote that I do in fact need? It's getting colder out & I leave in the wee-early morning hours for work & would love to have that remote start function working to warm up the car before heading off to work. Any help would be greatly appreciated! Thanks, Jerry