The most likely culprit is the battery. There are many cheap and poor quality batteries on the market. I would certainly try a new one or preferably, a known-good battery.
If that doesn't solve your problem, then you likely have a defective charge circuit on the logic board. It could be as simple as the battery gas gauge line having a blown or dislodged filter or it could be at the Tristar/Tigris chip level. Those are not DIY repairs and you should seek out an experienced micro-solderer if you don't have the tools or experience.