My battery is not charged. The only way to operate is to plug the computer in
Is your MacBook a plastic one made before 2008? Did you buy a new charger for it at some point after 2008? If so, the issue could be an outdated System Management Controller (SMC).

For some reason, the SMC's in the pre-'08 MacBooks will not allow charging via a Magsafe cable made after 2008. It will run off of it, but it will not charge.

Fortunately, Apple has a patch. Download the SMC firmware updated located here, and your MacBook should start charging from the newer charger.