The only way to fix it is to send it to the company SONY.They are the only place that does maintenance of that kind.
The above is the official answer... but if you do a little research you will soon realise that it is simply not true.
There are any number of local and national companies that offer console repair at much lower prices than sony will. of course SONY would have you believe that this is not safe because it is a difficult job and requires a pro. Again not true, all that is required are spare parts (normally a mother board costing £39.99 or around $75) and these parts take no more skill to attach than it takes to clip in that battery. Unfortunately they are only offered at the above price to trade stockist so you cant just do it yourself.
one thing you can do, and something that has worked for allot of People is this.
1. First of all DO NOT attempt to power up, this is not because you will short circuit and have big blue sparks flying everywhere (5V is way to little power for that) but because you will oxidize the contacts by electrolysis. Most of the contacts will be Copper, Nickel, Aluminum, or a Nickles used in Solder. All of these will oxidize quickly as only a small amount is present, and there oxides will not conduct, or in the case of some oxides of alloys will conduct far less. Either way your screwed because you've just destroyed your mother board and probably you battery management chip as well.
2. Remove any games that might be in the PSP, remove your memory card, and remove your battery. Leave all of the slots and the drive open (if you have a screw driver small enough remove the UMD drive cover all together withe the small screw on the bottom of the PSP and the 2 screws inside the drive slot).
3. Leave your console standing upside down balanced on the open UMD door in a warm dry place for about 3 days.
4. Try and turn it on If it does not work wait a weak or two than charge it.
One other method that can be very effective is to dunk your PSP in a box of dry ice. This should absorb all of the water. But be sure to let it warm up a bit before you attempt to play it as dry ice burns like hot coals.
if it still doesn't work send it off for repairs.
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It is classed as water damage, and probably needs to be replaced. A water damage specialist could fix the damage, but replacing it is probably a better choice.
Bring your PSP to a game store (like Gamestop) and ask them to fix it.
delete the data and puted in your psp
Go to the repair shop that it can fix your psp. If you don't see one find someplace else
Charge it...