I know this is old, but for those looking for this info, here is the fix on a DSI. I just fixed my daughters.
Take all the screws out of the back case, including the two under the rubber bumpers. Remove the battery. Disconnect the wire. Don't be scared, it unplugs off the board really easy. If you put the game down on the table, card slot towards you, you will see a little T cut out of the metal case. There is a spring type of wire that hooked the T on mine. That was the problem. Carefully pry the T so that the spring is underneath it again and it will work again. You will need a really small tool to pry it with. I would buy a small tool before trying it with a big one and messing something up.
It works!
Chris Fitzsimmons
February 2011