John Price, first off it's water damaged so no Apple will not repair/replace it for free. Second, as with any other liquid immersed device you need to follow a few steps for proper trouble shooting.
stop continuing to try to charge, sync or otherwise use your phone. This potentially can make a bad situation worse.
The very first step I would take is to disassemble your phone. Use this teardown to help you disassemble your phone. Take a careful and close look at all components and connectors. Truly assess the damage. Look for major corrosion, evaluate the pins in the connectors etc,. Take a look at all connectors as well as cable ends. You will have to remove all the EMI shields. If you do not remove the shields, you are not cleaning the board. Once you got the gross contamination cleaned, use 90%+ isopropyl alcohol and clean your parts some more. For a proper cleaning, use this guide. It was written for a Apple iPhone 3G but it is still pertinent to your phone as well. I can not stress the importance of a good cleaning enough, so do it over and over while replacing the alcohol after each cleaning. Do not use compressed air for the cleaning since that can drive liquid as well as corrosion particles into areas that will cause trouble later on. Do not use drinking water, if you need to use water, use sterile water. Also, you do not need to leave it to dry for a day. Isopropyl alcohol in the higher concentration will evaporate quickly and dissipate the water. The importance here is the cleaning. It would of course be best to get it professionally cleaned Do not forget to replace the battery. This is a must and not an option. It will fail if you do not take care of it now. After that reassemble your phone and re-evaluate. For as long as you have not cleaned your board and replaced the battery, everything is just a guess. Keep in mind that water damage is the hardest to troubleshoot and to repair. Hope this helps, good luck.