Have you tried resetting the System Management Controller? That is a good first step for power related issues such as this. You may also want to try cleaning the connection points between the battery and the computer.
If that doesn't do it and you have already tried replacing the battery, then you are looking at a hardware issue with the computer itself.
Best of luck.
Just for future reference, you should not reset the SMC more than once.
Your first post is a little ambiguous. Did you try using a different battery, or simply taking the one you have out and putting it back in again? If you have already tried a different battery, then there is no point in doing so again. The problem is with the computer. Which part will require replacement is not something I can tell you.
At this point I would contact Apple by going to http://expresslane.apple.com if you are in a country that supports it, or call the appropriate phone number on this page and see what they will charge for hardware service on the MacBook. Alternatively, carry the MacBook in to an Apple retail store or service provider to ask for an estimate. Be sure to make an appointment before going in to the stores or you may spend a long time waiting to talk to a Mac Genius.
It may turn out that the repair would cost more than the MacBook is worth, in which case you'll want to look at a new computer. The MacBook Airs are very nice.