Is this a 5-speed manual or auto box? If it's a manual transmission, put the car in 3rd gear and rock the car a little... This will free the starter gear being stuck to the flywheel. I suspect the little gear at the end of the starter is probably stuck and not moving back and forth like it should because due to age of the starter.
I would still jump start the car while cranking over the motor with the new battery. I just helped my next door neighbor with the exact starting problem on his 325i last week.