The button is stuck in the "pressed" position. To get my 3DS to respond as if it weren't being press, I have to pull the edge of the button up. When it goes back down, I do not hear the clicking sound the other 3 shoulder buttons make when they're pressed. The button is stuck down on the right, away from the center of the system. I've uploaded some images as well.
http://imgur.com/a/byG8P
The first and 3rd images are of my L button, which isn't broken. They're there for quick reference.