alright man, ive literally just installed custom firmware on a phat and a slim psp succesfully. try this - plug your psp into the mains, and make sure the battery is charging. switch the psp on, and the remove your normal battery and put in your tool battery. and just leave it. leave it on and the tool battery will charge. you can go into system settings>battery imformation, it should tell you its charging and how much charge there is.
also, where did you buy it from?