As mentioned, disassembly will be required if it's going to last at all. Disassemble (including removing the covers on the logic board) and wash the board and other components (not LCD or battery) with distilled water (ithis what the factory uses) or isopropyl alcohol, and dry with hot air (hairdryer). Put it in a tight container with a good desiccant (regular rice is not a good enough desiccant to work, though if you dry it mostly out 5 minute rice may). Leave in overnight.
A better desiccant, and one that's easy to get, is made from Epsom salts. Fill a shallow pan with an inch of Epsom salt. Bake for 2 hours at 400F. Remove, immediately crack up the resulting sheet of homemade desiccant with a heavy knife or hammer, then put it in a sealed container. Wrap your parts in a paper towel and throw them in the container. Remove after an hour or two.
As for the screen, if it looks odd/shiny at spots, especially with white backgrounds, there's water between the backlight film and LCD. Carefully remove the backlight (leaving the flex attached) and films/filters and dry each off by patting. If you need to clean pat with distilled water. DO NOT RUB. It will bend the film and ruin it. Re-assemble.