Instructions
Ensure that your battery is inserted correctly.
Carefully check that the power cord is not damaged.
If there is no damage to the power cord, plug your adaptor into a different outlet to be sure the outlet is not the problem.
If available, try the battery in a different PSP to ensure that the issue is with the battery and not the PSP system itself.
If available, try inserting a different battery into your PSP system and check for power. If your system powers up, replace your battery pack.
Check your PSP with the battery pack removed and the AC adaptor plugged into an outlet. If your system powers up, replace your battery.
Return your PSP for service if none of these steps work.