I have a Toyota Camry 2011 and two remote keys. One of the keys was soaked with water two years ago. Of course, it is not working. I went to a dealer and they failed to recover it.
Is there something I can try to fix it myself?
If you can access the electronics soon after they get wet, the chances are pretty good to keep it working. Unfortunately, after all this time, it's kind of a long shot.
There are three major things that happen when you get a circuit board wet:
The battery voltage can short across to the wrong parts of the circuit. This will cause it to fail, but seldom does any lasting damage.
The metal parts of the circuit will corrode. This is generally what kills the circuit. The corrosion can be conductive, and so will cause permanent shorts on the circuit board. This is especially common between pins of an integrated circuit, because they are so close together. Severe corrosion can actually eat though the the metal, causing open circuits.
The battery will start draining rapidly. In addition to killing the battery, the current flow really speeds up the corrosion process. In an extreme case, a battery will leak or explode. But I've never heard of that happening with small coin-cell batteries.
Anyway, enough of the problems. Here's what to do when a circuit gets wet:
Take care of it immediately. The longer you wait, the more likely that it can't be fixed. Five minutes is way better than fifteen :)
Remove the case. It's important to get the water off of the board quickly, and it will never evaporate when there's no airflow.
Remove the battery, if possible.
Get the water off of the circuit. This is more difficult than it sounds, because it won't come out from underneath the chips on the circuit board. One good way is to dump rubbing alcohol (99%, not 70%) over the board. It will wash the water away, and then evaporate very quickly. Also, this will remove any salts or contaminants that were in the water. Don't use rubbing alcohol if you weren't able to remove the battery!
Let it dry. If you were able to use 99% rubbing alcohol, this should take less than an hour. If not, give a full day of two to completely dry out. Putting it on a sunny windowsill would help.
Put it all back together.
I've done this with a half-dozen usb keys, a rental car key (that I swam with in Hawaii!), and the guts of a remote-controller helicopter. They all recovered :)
For your specific case, I'd try to scrub the corrosion off of the board and the battery contacts. For the circuit board, use an old toothbrush with 99% rubbing alcohol. For the battery contacts, you can be more forceful :)
I accidentally ran the smart key for my '09 Jaguar XF supercharged sedan through the washing machine once. It was submerged in water for about 10 minutes until I found it. I was able to fix it by opening the shell and removing all the contents. A ran a blow dryer over all the pieces until they were completely dry (at least they appeared to be) before putting them back together, and it worked.
One thing to consider before you go too deeply into this resurection effort. You can buy replacements on eBay for very little money (I got mine for $20 US) and the steps to marry it to your car are available online. The Toyota dealer wanted $80 just to program it. There are options to just replace it that are cheap enough that it's not worth the effort to resurrect this.