Charging through USB port can be problematic: when it enters sleep mode or is shut off the reader isn't charged at all. Plus, if the battery's too empty it won't be able to charge it.
What kind of charger did you buy? If it's one with an USB plug it won't work. You need to get a PSP charger (doesn't have to be Sony) with a round tip. If you haven't got one maybe family or a friend has one you can borrow.
If it still doesn't want to charge I would contact Sony in your country anyway to see if they can help, you never know (although with Sony I wouldn't get my hopes up).
Good luck!
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