The problem could be the prong inside the charging port. It's common with a lot of AC charging electronics with connectors like that. If you violently shove the charger in or rip it out you can sometimes push the prong too far, and the prong inside the PSP won't make a connection. This happened to my 3000. You could try opening it and moving the prong back to its original position or just buy this charger which charges the battery externally
The new charger solved my problem. It also allows you to charge a second battery on standby while you're using a different battery. It works with 1000, 2000, and 3000. But you have to use your cord from the old charger to plug it into the wall. Also, you might want to peek inside your AC charging port on the system to see if the prong is unusually recessed before you go spending money, because it could just be dud batteries. Hope this helped.
Well, when you do come into a little bit of money. I picked up one of these to charge my spare battery and it's cheap and official.
https://www.amazon.com/dp/B000X2BAOK/ref=cm_sw_em_r_mt_dp_RJxpFb1N7E8GN