Your Wii is not broken. Nintendo just pulled another Pokemon, crappy save battery edition, where everything erases. If it is truly the controller, check if their is dust or the settings. Otherwise call Nintendo and tell them about the situation. Of course it is Nintendo, and all of your official Nintendo, quality of seal products are on the thing. Especially if you Download pay.
Imagine a vast future, where ten-thousand Wii units, sit broken, while I am still playing my GCN games, from their CD's and cartridges.
Sega would never allow such crap to occur. Sure they spent funds on crap, like an External DVD-player. Sure the Dreamcast could have played DVD's ( but then again phuck dvds, VCD's are the 411. Sure SEGA messed on those decisions, but at least my Dreamcast, and Saturn, and Genesis can keep, going, and going, and going, and going.
Seriously check your warrenty. Check other peeps sit. Call them about it. To see if you can send it in, and retain your data ( if everything is legit, get it, legit ). Otherwise hoar your Wii out to a repair person, get everything off, and see what can work, and sell the thing for a penny, with free shipping of course.