Replacing the battery would have no effect on the electronic shift. Sounds to me like you need to clean out your hubs. They are vacuum operated, and if they get debris in them, they won't want to engage/disengage. My 03' did it often, after going through large puddles and mud.
Swapping a manual T case in, shouldn't require any fabrication. It should bolt right up. The only fabing involved, would be cutting the hole, and for mounting the bezel/boot setup.
If I'm wrong about this, please correct me:thumbsup: