Use one of those high pressure hoses in a diy carwash.
Back up as much data as you can on an SD card, because it sounds like you may have to send it off to Nintendo. It should be noted that Smash Bros Brawl, Mario Kart Wii, and Animal Crossing City Folk data all cannot be moved from the system memory, so if you have any of those, you're screwed. Everything else should transfer though.