There's a bit of dirt stuck under my PSP screen. I've tried spraying through the back with compressed air, but the dirt didn't even budge. I don't have a small enough screwdriver to reach down and get some of the screw in order to open in completely, and frankly I don't really want to, all those tiny buttons would fall out of place.

Call Sony? That's the only advice I can give. I don't have a PSP.