Original post by: arbaman ,
Best thing you can do is open up the bottom and disconnect the battery from the logic board. The Mac would be working flawlessly even without battery if your logic board has not been damaged and it's just a battery issue. That will give you the necessary answer whether to invest in a new battery or else. Consider also that there are professionals specialized in component level repairs who would be able to fix the logic board without the need of a full replacement.