Kodak easy Share z650 / lack of support

I contacted Kodak Easy Share about my new Z650 Easy Share zoom digital camera on Jan 14 after receiving it as a Christmas gift. After taking 200 pictures, the battery was no longer good. It came with Lithium CRV3 3V, which according to one of their replies is "good for approximately 370 pictures". Since I only took 200 pictures, and it was a new camera, I asked for a replacement battery after reiterating what kind of battery it was and the camera was brand new. The next reply was that "this battery should last for 370 pictures, however it will depend how long you leave the camera open after taking a picture or how often you take a picture". All I wanted was one measly $6.99 battery replacement, after someone already spent $250.00 for a camera. Obviously, good customer relations to not worth $6.99 to such a large company.