How do I fix the backlight not working after water damage?

My iPhone recently got a little wet from the rain (in my backpack), and refused to charge. I took it in to the Apple Store and the guy noticed the liquid indicator in the dock was red. Not wanting to spend $200 to replace it, I took it apart and cleaned the connections and got it working again. The phone is fully functional, except for the backlight on the display. After researching online, it appears that simply replacing the display does not solve the issue for people.

What can I do to fix the backlight?!

Any help is greatly appreciated.