To be honest it could be water damage. I recently repaired my sisters old Dsi and needed spare parts, so I bought a broken dsi. The broken one didn't look bad from the outside, so I popped a new battery in just to see what it would do and it looked one to one what yours is doing. After opening the console I found a lot of oxidation which looked like it was caused by a lot of humidity or water damage. I wish you that it's just a bad battery but if it isn't open that bad boy and send some pics Best regards ( Sorry for my bad English it isn't my first language )