Chosen Solution
Made a mistake trying to fix my psp go and made it worse, L trigger no longer works, any way to reattach connector to logic board?
aaron, the angle of the pictures is a bit distorting. It appears as if your solder pads are still in place. I would resolder the connector. You will need a good soldering iron with a small tip to accomplish that, but not impossible. If you are unsure on how to do it, any decent electronics shop should be able to fix that for you. Hope this helps, good luck.
The only way to fix it would be by soldering.