I'm seriously wondering if this has ever been attempted with any model of DS or 3DS. (For instance I have a spare DSi I could try experimenting this with.) But ideally I'd ask a tech repair person or modder to do it. My idea is to remove the top screen half (removing the clamshell in other words) to make the system like a PSP.
There's this video titled "Stupid Kid Breaks Nintendo DS in HALF!" http://www.youtube.com/watch?v=1Qb5jL2lmeU and in that vid, removing the top screen instantly caused the bottom screen to stop working as well. If so then that might be a problem.
"This DS was broken for 2 years now, and I wanted to cut off the broken top screen so I could use the bottom half as a gameboy. After I cut it, the bottom half didnt work."
Interesting that his idea was not unlike mine.