I don't know what that part is.
It's possible to repair these if there is not more systematic damage. However, there are two challenges first.
1. Identify the part.
2. Obtain the part.
The first one could be tricky. I don't do enough SMD work to recognize it as something obvious or common, but it could be. Most of the parts in most electronics are common shit like caps and standard ICs. Some of them are obfuscated - they're common and can be obtained IF you can figure out what it is. Others are custom, and not something you can reasonably obtain (cost would likely be >> just buying a new DS).
If you can identify the part and it's not a custom IC, obtaining and fixing it is just a matter of finding someone with the experience to do the job.