You may want to try taking the battery out and putting it back in, just to make sure it is firmly in place. If that doesn't help, do a switch with a friend with the batteries (if you know someone else with a PSP) just in case it is the battery at fault.
If your PSP still doesn't work after that you are left with no choice but to contact Sony's tech support about repairs- there would be nothing you could do yourself unless you are very handy at handling electronics repairs.