Okay, so I just had a 24 minute conversation with "Lem" the nintendo customer service representative. He was really helpful, but kinda slow at his job.. I was getting kinda annoyed how long the process was taking.
The cost to repair the DS would be $75 or the other option would be to replace the DS for $90 for a factory refurbished unit that comes with a 1 year warranty. You have to pay for your own shipping to one of their three repair centers in the U.S. (washington, california, and new york)
The options that were given to me didn't sound so great. $75 bucks to repair the DS I bought for $129? I don't think so. I might as well buy another DS on ebay or something. My DS is over a year old so that might have something to do with the super high costs. So if your DS is still fairly new then you might have a chance to get a free repair.
By the way if you want to find out for yourself you can call the Nintendo Consumer Service Department at 1-800-255-3700. Representatives are available every day from 6 a.m. to 7 p.m. Pacific time.