Battery "Not Charging" in MacBook
Here are the steps that Apple Technical Support gave to me before issuing a new battery to me. My MacBook was not under AppleCare, but it is less than 1 year old. However, it sounded like Apple would still have issued a battery to me if it was more than a year old.
Check the battery each time before moving to the next step:
1) Update software (click the apple in the upper left, select "software update."
2) Reset the System Management Controller (SMC) by shutting down, disconnecting the power adapter, removing the battery, and holding down the power button for 5 seconds. Then, insert the battery, attach the power cord, and turn on the computer.
http://support.apple.com/kb/HT1411
3) Reset the PRAM by doing the following:
Shut down the computer. Turn on the computer. Immediately after turning on the computer, hold down these four buttons: P, R, option, command.
http://support.apple.com/kb/HT1379
4) After these did not work, Tech Support had me send my computer info to Apple to verify my battery cycle number. (System Profiler>>File Menu>>Send to Apple). My battery had about 100 cycles on it.