Which version DS is it? I heard that the DS lite has some problems with the shoulder buttons and they wear out pretty quickly.
As for getting it repaired... since the warranty has expired, there'd be a fee to get it fixed by Nintendo... that or they won't bother at all citing it as being normal wear and tear rather than a defect with the system. Of course, Nintendo has been known to be pretty good with these sorts of things so it's probably worth a try to contact them directly and see what they say.
If all else fails, you're better off getting a second hand DS from somewhere as a replacement if you can find one that's cheap enough.