The connection for the battery inside the system or the connector on the charger?

I recently bought a used PSP 1000 from my friend and it worked fine until I came to charge it. When you insert the charger, the orange light comes on for a few seconds and then goes off. This seems to usually happen if the connection on the wire moves slightly but even when I keep it still, it stops charging soon after.

To try and get around this problem, I have removed the battery and have just been playing with the charger in. This works fine most of the time but it can easily shut off if the end of the wire is knocked and I would like to be able to actually use it as a portable system. I also can't charge it via USB since it's the 1000 model.

I'm using a 5V, 2000mA charger which is what the system needs and a 3.6 V, 1800mAh battery (shown on the right of this image).

I would like to know if it's the charger or the battery that's the problem or if it's the connections inside the system.

 Can anyone help me?

(I can buy a new charger and/or battery if necessary and if all else fails, I do have the option of returning to my friend.)

Thanks in advance. 

The Vita can only run downloaded PSP games since it uses game cards rather than the PSP's UMDs. It may enhance the game slightly, similar to how a blu ray player will enhance DVD quality but I don't think it will make much difference, if any.

I think it was Doom which I downloaded was I was 11 or 12. Either that or Call of Duty but the first one I owned was Turok: Rage Wars!

Mine is pokemon Soul silver version!:)