The holes are on the edge of the silver disc on the face of the lock cylinder, kind of right on the inner edge of the black ring.
That may be a good position for it to get stuck in, as far as trying to remove the lock cylinder and saving that part. I believe that one has 2 holes, directly across from each other, let me know if I'm wrong and there's only 1. Usually the steering wheel lock assembly is what's seized, not the lock cylinder, although most techs want to replace both, just to be safe.

Gilly

PS NO, the battery has nothin to do with it.