Just a note about the hit you got: fatty tissue and stiff white hair sounds like a brisket shot to me. There's quite a bit of fat right under the skin on the sternum of a deer and that's about what you get with a hit there. I wouldn't worry about the deer dying with that kind of wound. Since you didn't find any blood to speak of, I would be pretty sure it will survive OK.
Hope you get the gun issue resolved.