WELCOME TO DCEMU!
Your PSP sounds completely knackered to me...
Copy and paste the link. When my psp died, this is what i did and it is 100% genuine.
Basically, any thing wrong with the psp, ANYTHING, and they will replace it for a reconditioned one at YOUR doorstep. I did wonder about the condition it would be in, but it was mint. And its not a bad price either definately something to consider