You did the right thing by removing the battery and letting it dry out. To try fixing this yourself at this point, you should open up your phone. Unfortunately we don't have a guide on how to open that phone, so when you open it, please [http://www.ifixit.com/Guide/new|show us how you did it]!
Once you have it open and you're at a step where you can see the logic board (the main circuit board in the phone), you should use some strong isopropyl alcohol (90%+) and a soft brush to remove any white-ish residue you see. Let the device dry <thoroughly> to make sure all liquid is gone (this should take less than a day in a warm, dry place if the device is opened up. Putting the device in a bag of rice can also be useful at this point.) When it is dry, put it back together, and you will have your best chance of it working.