I was wondering how to test the logic board?

Colby A, there is no way to say that the board is probably good. It all depends where on the board a short circuit may have occurred. If you want to repair your phone yourself, I strongly suggest that you do not try to restart the phone. This may further damage your phone. You also do not want to charge it any further. The next thing to do is to clean it. Disassemble your phone using these guides. Once it is disassembled, you do need to clean it properly. You will need high grade isopropyl alcohol and a soft brush. Use this guide to see how to clean it. Even so it was written for a 3G all the points are still pertinent to your phone. While you are cleaning it, check for any broken, missing or burned looking components. When it is properly cleaned, replace the battery. All these steps are to avoid delayed failure caused by corrosion. Once all this is done, reassemble your phone and reevaluate. Water damage is the hardest to diagnose and the hardest to repair. Yes, it "may" only be the digitizer right now,but it will be death by corrosion later on. Hope this helps, good luck.