Had the same problem with my sons 3DS.
Check the ribbons behind the top LCD screen. They come loose from opening and closing the DS and can cause a short. In mine, I was lucky and it was just a loose ribbon so it could be fixed.
To expose the back of the top LCD screen, follow ifixit instructions. Be careful removing the screws. The speaker magnets are quite strong and the screws are attracted to them which could tear the speaker cone.
Check to see that all the small ribbons under the speakers (volume, camera, 3D) are properly seated in the connectors. The connectors are like buckles. To reset a loose ribbon, gently lift the top of the connector latch opposite of where the ribbon is inserted. Carefully re-insert any loose ribbons and close the latch.
I then created some slack in the main ribbon at the bottom and taped it down so it wouldn't move when the DS was opened and closed.
This solution worked for me.