Unfortunately your options are limited.
Did you try different games? Are there any frays in the power adapter? Is the power cable plugged into a power strip?
The other options are to pop it open to look for anything super obvious going on inside but that voids not only any remaining implied warranty, but Nintendo won't even repair it if they see signs of the case being opened.
My opinion -- return it if you can. Otherwise, if all else fails, sell it as-is on eBay for parts. They go as high as $40-$60 shipped.