Three of my kids received Nintendo DS Lites for Christmas as well. One stopped powering on and we had it replaced within 3 days with advance replacement progam from Nintendo. Then shortly after we received it the hinge broke. They replaced that one as well no charge. Then another one of our system's hinges broke and they also replaced that one free of charge. They were very nice about it. She informed me that they do not usually cover the hinges but she offered to do it free of charge. I was fully expecting to pay for the repair.
This was probably the fastest and easiet repair we have ever had on anything.