I would surmise you have the around view system. Finding a replacement unit will be tough as it was just introduced on the 2012 models. To make things more difficult, I believe there's a slight size difference too, with '12 unit being a tad larger.
You'd have to pull the unit and open it to get a part number, but I dunno if you can order a replacement screen. There's a seller on ebay that deals in parts off wrecked Rogue's, but it may take a while before he gets something in.
If there's no difference in the screen, you might be able to swap out one from an '11. I did a google search and it seems that if you can find a compatible screen, you should be able to swap them.