Oh Thank god. I have been searching the net all week for this problem.
My Daughters DS has this exact same problem. To make it clear, she uses a DS Lite, with no modifications, nothing unusual at all. Just plays normal games (mainly club penguin and Nintendogs) Last week, she said her DS was going funny. I looked and it was fine, then suddenly while she was playing, both screens went mega-bright, like white, and all you could see was some sketchy outlines of things in black lines (like OP said, a bit negative like).
Then when she touched the screen again it went back to normal, then back to white, and keeps flicking between the two, (mostly when you touch the screen, but sometimes if you just press one of the buttons)
So it isn't a problem caused by using any non Nintendo stuff, and it definitely happens on both screens together.
Have any of you with this problem found a solution yet, or have you sent it off to Nintendo and had an engineers report back on it.
Please, please let me know, as ours is out of warranty, and I can't afford a repair at the moment.
Thanks