We have the original PSP (called the PSP-1000) and Calvin fixed it. It had a sticky analog joystick. Looking at Youtube and Google, someone recommended just lifting and blowing the gunk out. That didn’t work.
So disassembly is just 7 screws detailed here
Then another site explains how to take out the two screws holding the joystick and then it is $12 to replace. In our case just taking it apart freed it. And we lost a nifty USB to charger system. Since the PSP original just needs 5V and 2 amps, it should work with most iPad chargers with the right adapter. It is another $5 strange accessory.