Yes, You can pull the BCM. You will first want to disconnected the negative battery cable and be certain it does not slip and hit any part of the car that can carry electrical current. Look at post #9, and click on the link. It will show you a picture of exactly what you are looking at. The link talks about the RCM, but you want the BCM. Once you have the lid off the large plastic box the BCM is the one close to the fender. It will be difficult to pull the wired connectors off of the module. Take your time and do it carefully; Do not pull on the wires. Look for any locking clips on the sides of the electrical connectors which must be disengaged before you pull. Get a hold of the plastic connector and pull up on it.

If all this seems too much. Try an independent european specialist garage. Let them first test for power at fuse #19 and if that is good then disconnect the battery and change out the BCM. One hour labor max or their minimum charge. If you have damage to your wiring because of rodents, then you are into much more in the cost to repair.
GOOD LUCK