i fixed this prob in my psp by taking out the small clear rubber connector between thE analog stick and the pcb and cleaning it with a damp cloth then drying it and putting it back in... (be sure to put it back in correctly) NOW THE ANALOG STICK IS WORKING PERFECTLY :-)
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http://www.ifixit.com/Guide/Repair/Installing-PSP-1000-Buttons/1784/1 This guide should show you how to do it. You might only have to follow up to the end of the second page (The end of the Front Case).
i fixed this prob in my psp by taking out the small clear rubber connector between thE analog stick and the pcb and cleaning it with a damp cloth then drying it and putting it back in... (be sure to put it back in correctly) NOW THE ANALOG STICK IS WORKING PERFECTLY :-)