You can still download from the PSP store, but you have to purchase the games on a different device.
You must be using firmware 6.61. It can be custom or official. Going into the store always gives an error and nothing appears but the store does load. It's just blank. If you go to the Playstation Store online on a computer/tablet/phone and purchase a title, it will appear in your download list on your PSP when you reload it. I made a boring video if you want to waste a few minutes.
Have fun!
Jake.
Have fun!
Jake.