Check to make sure the battery inside is firmly in place, first of all- it is possible it may not be fully connecting. If you are sure it is fully in place there is a chance the battery itself may be at fault and needs replacing- if you know someone else with a PSP, try doing a battery swap with them.
If, even after swapping the battery, it doesn't work then the problem is elsewhere in the PSP (most likely on the motherboard itself) which may mean a call to Sony regarding repairs.