Well you don't need the box to get repairs. If it's really bothering you, then call AppleCare up. I'm just warning you now though, they don't typically help out all that much with stuck pixels.
If they're stuck and not dead (coloured, not black) and it sounds like they are, then try rubbing them gently to bring 'em back to life. Also, play a movie behind them overnight. Sometimes the rapid colour changing can help too.