i would HIGHLY Suggest (yes i hate bring old threads) is you HAVE TO take it apart.
but just to get the back...cause i just almost killed my DSI using the suggested answer (got my L&R buttons "Working")
use just compressed Air to get the dust out! when you do this you can also bend the buttons up some soo they can have better contact. and also get a hard deep into it if you have to press hard
reason is i wanted to play some DS games not on my 3DS as i tried to fix it now....reason cause i'm restarting my Pokemon saves on the DS and i needed a trade thing...since i have a Pro Tech Tool Kit i can just open it up...
if you dont...try the Most Helpful Answer...but BECAREFUL OF L OR R!!! that is the side of the ribbon for the top screen....that jangles...no top screen or sound!