Richard Kanady, besides the excellent answer provided by Gigabit 878 I would like to add a few things.
"The phone has sat for three days in our very warm garage." this will expedite corrosion damage. What you want to do, is to prevent this.
I suggest that the very first thing you want to do is to not try to restart, sync or charge the phone. This may further damage your phone. 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 must remove all the EM shields of your board or you are not cleaning it properly. You will need high grade (90%+) 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. The better way of cleaning would of course be an ultrasonic cleaner. You may consider a professional opinion. for that you should contact @refectio He specializes in this type of repair. Once all this is done, reassemble your phone and reevaluate.Water damage is the hardest to diagnose and the toughest to repair since virtually any part may have failed regardless of how long it was submerged. Without getting your phone to turn on, you will not get to recover any of your images