open the PSP, (use ifixit to open the front panel).
then use a pincet to pick up the little silicon pad, turn it 180 degrees. (look if you see tiny spots wich are the connectors)
then remove the joystick from the case, clean the connectors.
screw it back in.
thighten thighten thefront panel to its limit. (use a precision screwdriver)
make sure its realy really thight.
then open up the browser for testing.
if the problem still occurs thighten it even more. (make sure to be save and not break the plastic screw holders in the top case)
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after that recalibrate it.
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if the problem still occurs buy a replacement joystick (cost about 2$)
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then repeat the steps i said.
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(this solved it in my case) (i have a frankenPSP 1003/4) (made 2 PSP into 1 working)