I have custom firmware on my PSP wheelo, and the charging option works fine.
Try going to System Settings and see if "USB Charge" is set to on, and then try the USB cable in the PSP.
This is a discussion on charge PSP by USB within the Sony PSP forums, part of the Gamers Lounge category; once upon a time i was able to charge the PSP via ...
Found this elsewhere,
To charge psp using a USB charging cable.
*1 - Turn your playstation portable On.
*2 - Go to Settings.
*3 - In the settings options go to System Settings.
*4- In the system settings,select USB charge and press the button.
*5 - Choose ON and press the button to enable USB charging.If at any time you wish to disable the USB charging,select OFF and press the button.
*6 - Now plug in the USB charging cable to your psp,and the other end to your PC,
laptop or other suitable USB device.
*7 - Go to settings and choose USB connection,press the button to place the system into USB charging mode.You now may notice a sound and the power indicator light will turn orange.Your system will now be starting to charge.
When using the USB charging option you may notice that the auto sleep feature may not work.