Hello, Sorry you're having problems. If the battery will not take or hold a charge, then this indicates the battery has failed and needs to be replaced. The battery for the 2DS can be purchased at the link below:
Follow the instructions below to change the battery
Notes:Do not attempt to remove the battery cover with anything other than the recommended type and size of screwdriver.Do not over tighten the screws. This may result in stripping them or cracking the housing.Depending on the model, the screws may be secured to the back panel. If this is the case, simply losen the screws.A #00 cross-head (+) screwdriver will be required to change the battery pack on the Nintendo 3DS, Nintendo 3DS XL, and Nintendo 2DS. A #0 cross-head (+) screwdriver will be required to change the battery pack on the New Nintendo 3DS XL.
Additionally the link below outlines the process with pictures:
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