Check fuse F100, this is where fuse 45 gets it power from, by the battery for corrosion to make sure corrosion is not bridging two or more circuits. Probably not but only takes a few minutes to check.
Continuity doesn't mean the wire can carry a load. If there is 1 strand of wire still good, it will pass the continuity check but when you apply power 1 strand is not enough to carry the electrical load.
Mine did not need to be coded. I installed this on my 2003 and I had to add two wires to the green plug and tap those into the "I bus". The closest I bus wires are at the LCM. Just make sure those two wires are there.
I'm always afraid that I'm going to break something yanking the door off. So, I found a universal torx extended bit that can get to the two screws with the door held partially open.