Whenever I go visit a GameStop or EB Games branch with a PSP kiosk, what will most often be broken on the PSP is the joystick. Whether this is due to excessive wear and tear or vandalism is anyone's guess, but of all the moving parts of the PSP, the joystick always seems to be the first to fall off.
So what do you do then? I'd suggest seeing if the warranty's still good and get it fixed that way, but chances are it'll involve either A.) a long-ass wait, or B.) money on your end to pay for initial shipping charges. Considering the inconvenience (and the likelihood that you've already voided your warranty anyway), one plucky PSP fan is offering a DIY alternative to having to wait on hold for a hour.
The guide is pretty simple and essentially just documents specific screws and pry points that you'll have to watch out for. But seeing as not everyone is willing to try their hand at sticking sharp objects into their $250 gadgets without some direction, this guide is a pretty good place to start.