The best chance you have to fix this is to take it apart and clean it. I use 91% Isopropyl Alcohol and a toothbrush. I also have a small spray bottle that I use to spray on the motherboard then scrub it gently with a toothbrush. You want to remove any corrosion that has taken place. This will also help to prevent further corrosion.
The first thing that needs to be cleaned is the motherboard. After you clean it you need to let it dry for a while. I put mine on the window sill and let them dry in the sun for a couple hours. After it's dry, re install it and see what happens. This will give you a better idea of what else may need to be done.
Doing all of this may or may not help. I have not had a lot of success cleaning water damaged 3DS motherboards, but I have fixed some that way. Since yours still turns on you have a better chance of fixing it using this method.
I hope this helps. Let me know if you have any other questions or need further help.