Annalise Brawn part off this is because of "dried it out for over a week in rice". Rice does not work. It does not do anything and is the equivalent of doing nothing. What you are running into is corrossion damage. Hopefully it is just your display assembly that has failed and not the components on the logic board. you want to treat this just like any other water damaged device.
For now do not continue to use your phone. Do not power it on and do not try to charge or sync it. The disassemble your phone using these guides. Once it is disassembled, you do need to clean it properly. ON this model you must remove the EMI shields for proper cleaning. 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 an iPhone 3G all the points are still pertinent to your phone. Of course, if you have access to an ultrasonic cleaner, take advantage of it. 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. In your case you can try a new dispaly assembly and see if that works. If you do not treat the water damage, your phone will definitely continue to corrode and slowly die.