Darryl Whitmore sounds like you are dealing with the after effects of the water damage. I'd start with that. Use [[Topic:Samsung Galaxy S III|these guides]] to disassemble your phone. Once disassembled use [guide|5825|this guide] to help you clean your logic board. you have to remove all EMI shields. That guide was written for an iPhone but all the points are still pertinent to your phone as well. Of course if you have access to an ultrasonic cleaner then you want to get it cleaned that way. While you are cleaning it, pay close attention to the components on the logic board. Make sure that there are none missing or that you have a burned/charred looking component. Once it is cleaned, you do want to use a new battery. That way you have a known good starting point.
Now comes the fun part, troubleshooting what works and what does not. You will have to have a multimeter for that. Start off with the power section. Here is a document that flowcharts the no power on situation [document|2049] water damage is the hardest to diagnose and to repair since virtually any part my have failed. Definitely a challenge and a great exercise.