Hello,
I do not know for certain the issue you are facing, because I cannot physically look at the device, but with prior knowledge with tech, I can do my best. Here are some suggestions:
# If you can, remove the battery, then reinstall it to do a force shutdown.
# If that doesn’t work, try installing a new battery.
# If that doesn’t work, there is probably a issue on the inside, therefore requiring you to tear it apart.
I hope this helps, and you get your PSP up and running!