The whole thing is removable if you remove the screws under the plastic covers on the side (lift the lid and they are on each side of the bin). It will probably be easier to fix with it removed. (BTW the dash vents come with it as it is one piece.)
You will have to give the whole thing a good yank to get it out. There are some tabs by the vents holding it in once the two screws are removed. On the back of the bin are two screws that hold the door on. It seems kind of common for those to come loose.