You got to get sure your friend's Pandora kit works fine before we consider your PSP's faulty.
When you're sure of it (by trying it on another PSP), we'll start to look for the reason why it doesn't work with your unit.
Can't find any threads about this particular issue on GBAtemp or the wider intarwebz. Saw one video on YouTube that seemed relevant, but it was some dude with the same issue, no solutions offered in the comments. :/