My PSP won't hold its charge anymore. We tried a

Sounds like the dc jack is bad in the psp. From a place like this you can order a new psp dc jack:

http://www.portatronics.com/product_info.php?info=p422_PSP-DC-In-Jack.html

This site shows you how to open up the psp:
http://forums.afterdawn.com/thread_view.cfm/370436

Its cheap to get the dc jack the time consuming part is taking it apart and taking out the old one and putting in the new one.

If you do all of this and the known good battery still won't chage then that means the board is bad and would need to be replaced.

check ebay