Few possible options here. Likely a combo of trying to use the ac adapter and pandora at the same time. You don't want to do that.
Remove all sources of power. Ac adapter and battery. Put in JUST the ac adapter and attempt to power on. It should power on from there. If that's the case, wait until your at your psp's main menu, then put in the pandora's battery and allow it to charge for a bit.
With that done, remember you need to remove the ac adapter, remove pandora, hold any button combo you have set up (normally L trigger) and put in pandora. If it's still powering on to only a black screen the memstick simply isn't set up correctly. Pretty much that simple.
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