I had the same problem , my psp 3004 was not detecting the battery, and the solution I found on internet was to change de 3.3v 0.2f condenser. This is the reference of the one I bought on aliexpress in case it expires:
***Condensador Super Farad, SMD, 3,3 V, 0.2f, DSK-3R3K204T614***
[link|https://es.aliexpress.com/item/1005004602835836.html?spm=a2g0o.order_list.order_list_main.798.4479194d3n2F8R&gatewayAdapt=glo2esp|https://es.aliexpress.com/item/1005004602835836.html?spm=a2g0o.order_list.order_list_main.798.4479194d3n2F8R&gatewayAdapt=glo2esp|new_window=true]