Tell the Dr your symptoms. Did you take the battery out and try just the charger and psp? If you did try moving or rotating the charger while plugged in if you get a blip it's the charger contacts my be dirty or messed up.
The next step requires a device with a similar port. Which I don't think you own but you need to find away to see if the charger gives a current outside of licking the end. If you do find away but the battery won't charge it's the battery. I can find replacement batteries here in NY but I doubt you live anywhere near here.
Good luck, it rarely is the psp itself unless the contacts are bent or you've been bad to the psp and deserve not to have it working. The battery however is known for just stright up dying on people. I Myself own 3 psps of various model types and still collect more, Sony should really be doing something about the preservation of thses games on the perpriatary platform they made for it.
I still look at my MD players and get pissed that there's no way to use them. Outside of windows vista 32 bit. 64bit wont even recognize the program let alone the device.