Not having my PSP in front of me and not knowing what model you have, or what kind of computer or OS you are trying to do this with, I believe there may be an option to format the memory card from the PSP itself. I believe there has to be an option somewhere on the PSP to do this. My reasoning is that if you put in a brand new memory card, it needs to be prepared for use in the PSP. In other words, the PSP installs files on the memory card so it *knows* how to communicate with it. Basically, it installs a file system on it, much like your computer does when setting up the OS.
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Pull out the memory card and plug it into a card reader that is hooked to a computer. Then, as it shows up on the *My Computer* screen, right click on the memory card and select format. Be sure you have the right card selected for formatting, or you could hose your computer.
Hey, looks like your PSP may have one of these two problems. There are 2 screws on the backside of the PSP System on the side of the analog stick. If either of the screw is loose then the analog stick will move by itself. Second problem is the Analog Stick itself has been damaged. You can replace these very easily if you are good with tools and electronics.
Pull the battery out, put the whole thing in a can of uncooked rice for 8 hours, the put battery back in and try. And, Why post a question for a phone, in Video Game Consoles? lol ^^
First thing you need to do, is make sure you have the newest firmware installed. Either via wifi connection, or by going to PSN.com and downloading the newest firmware to a thumb drive to install it manually Then the "STORE" option should be available. The other option it to sync it with a PS3 and visit the store, then install from the PS3.
It fairly easy to take it apart, but please note that there will be alot of small buttons, rubber cushions and guides that will come loose in the opening of the PSP. It could be dirt that cuase it to not fuction correctly or the pressure mechnism is warn out, but easy replaceable. The following videos might guide you how to.
It's most probably the analogue controller. If it's a PSP1000, 2000 or 3000 go to the web browser screen. Here you'll see a mouse pointer that can be controlled with the analogue controller. If it moves by itself then the analogue controller is faulty. Of not then it's the directional buttons.
Does the stick return to the center position when not in use or is it loose? If it won't return to the center position, then the stick will most likely need to be replaced. The PSP has to come apart for you to replace the stick. As for the 2 screws being loose? You would have to more permanently put them in, but then you may not be able to get them back out.
It is also possible that dirt/dust has gotten into the joystick area and is causing problems.