Instructions
Remove the battery and plug the PSP into the wall using the power adapter that was bundled with the device. If the PSP will not turn on when the battery is in, there is a good chance that the battery has been fully discharged and needs to be replaced.
Remove the memory card. If your PSP will not load content from the memory card or you are getting corrupted save error messages, you may have a bad or corrupted file on your memory card. If the PSP works without the memory card, you may need to format the memory card before using it in your PSP again. Check your owner's manual for specific formatting instructions.
Update the PSP firmware. If you are having trouble playing a new game, but can play old ones without issue, you may need to update your firmware in order to get the game to play. Connect to the Internet via a Wi-Fi hotspot. If an update is available, your PSP should notify you automatically, and you can download it directly by pressing the "X" button when the notification appears. Alternately, you can connect your PSP to a PC with an Internet connection and download the PSP update from the Sony website.
Check the UMD disc. If the plastic on the UMD's casing is damaged, you may need to see a repair specialist or replace the disc.
Hold the PSP upright. The PSP should not be played laying down, as this puts strain on the motor and can interfere with playback.