Chosen Solution

I am repairing a 3gs that had water damage. I took it apart down and gave the logic board a good soak in 90% alcohol, and gently scrubbed it down with a toothbrush (noticing and removing some corrosion that appeared on the 6r8 coil). Backlight worked for 3 days. This could help most people. I, however, am not most people. The backlight went out again. Soaked the logic board again in alcohol, overnight this time. Worked until I shut the phone off, then no backlight when I turned it on again. Any ideas on this one?

If you are certain you have a working LCD and that you cleaned the iPhone properly using this as your guide.. It was written for a 3G but does apply to your phone as well. If all that works out, I would go ahead and replace the coil. As you stated in your question " (noticing and removing some corrosion that appeared on the 6r8 coil)", there may be more damage on your coil. Hope this helps, good luck.