If I recall a good number of DS Lites were affected with hinge cracks. Nintendo later issued complimentary repairs under the one year warranty, since the issue was first noticed during the first months of the DS lite North American launch. They still offer free repairs under the warranty and they even issued a statement saying they would fix any DS with that problem.
I don't know how much it would cost outside the one-year warranty. But I would recommended to anyone to get it fixed especially if it is under warranty. I got my repaired DS within a week after sending it to a service center.