I don't recall what you need L and R for specifically but I assume you'll just need the triggers fixed. You should contact Nintendo since that's a fairly common issue.
Unless the flash cart leaves some super obvious traces on your system, I have no idea, I've never used one. And if that's case I guess you're just out of luck. 'Tis the cost you must pay. --- Work is for people who don't know how to fish! 3DS Friend Code: 1289-8728-7299