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Good luck finding pic related and having the ability to solder it properly, doing it wrong will fuck up your cartridge.
Even as you solder in a fresh battery you need to reconfigure the game's internal clock manually because the game will not recognize your new battery, there was an old program for the DS made for that.
Even if you did all of that you have to start a new game for everything to work properly again. The only way to save your files is to move it to an emulator.