@samgingo for now, stop continuing to try to charge, sync or otherwise use your phone. This potentially can make a bad situation worse.This may further damage your phone.
The next thing to do is to clean it. Since iFixit does not yet have a specific guide for this, use something like [https://www.youtube.com/watch?v=1krEl5yRm8w|this video] It'll work for your phone as well. Remove the main board and the charging board. You will have to remove all the EMI shields off those boards. If you do not remove the shields, you are not cleaning the board. As an FYI, I do no loner clean the sub-board (charging board) but replace it. That way I have a known-well starting point for any further troubleshooting.
Take a close look at all components and connectors to 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. Once you got any gross contamination cleaned, use 90%+ isopropyl alcohol and clean your parts some more. For a proper cleaning, use [guide|5825|this guide.] It was written for an Apple iPhone 3G but all the steps are 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. While you clean your boards, check for any obvious damage, like burned or missing components etc. The importance here is the cleaning.
When it is properly cleaned, replace the battery. This is a must and not an option. It will fail if you do not take care of it now. All these steps are to avoid delayed failure caused by corrosion. Best thing to do would be to clean it with an ultrasonic cleaner, but if you do not have access to one, this will at least help. Once all this is done, reassemble your phone and reevaluate. REpalce the sub-board (daughter board) with a new one. Until it is cleaned, everything will only be a guess. It is possible (most likely) that you have a bad display assembly which includes the touchscreen. [https://www.youtube.com/watch?v=6-go26Ml9Q0|this video] will show you how to replace the display. Replacing the display assembly may fix it. Even with all this, water damage has only a small chance to be fully repaired, but at least you can give it a try.