Help with analog stick!!

Ok here's the thing i have a psp that it works fine for a while after i turn it on but if i use or press the directional buttons ( up the analog stick) too much the analog stick will either start going down/right or it will stay still and respond fine in every direction except up/left that direction will move terribly slow and if i turn it off for a while and back on it will work fine for a while again. So i took out the analog stick and turned on the psp and the mouse pointer on the web browser will move down all the way when there is NO analog stick on the psp.. So the thing is i want to be sure that the analog stick is what i need to change or if it is any circuit or what. Please help so i can buy the proper replacement. THANKS.