Did the battery door break off (the hinges where it attaches to the body), or did it just COME off? It is removable for when you use a battery grip. Can you hold it in place while you turn on the camera? The camera will not turn on unless the cover is fully seated.
Either the cover broke or the hinges on the body broke. If you can't tell which, a camera repair shop can at least tell you. A broken cover can be easily replaced. Broken hinges on the body is a whole lot worse.
If you can't see what broke
