We'll there are a few ideas circulating how to fix the back light problem, in my personal experience i found that cleaning the contacts with alcohol fixed the problem on a few peoples phones i've fixed.
Follow this guide up to and including step 6: iPhone 3GS Display Replacement
You should now have 2 half's of an iPhone.
Where you unseated connectors 1 2 and 3, clean the connectors on the logic board and the connectors coming off the screen part (both parts of the connection) with alcohol, isopropyl.
What usually happens is that the "breaker" has dropped / left their phone in liquids that when dried out leave a residue or a build up of a certain other substance that doesn't conduct so the connection is broken on a few pins where the substance resides.
In your case there is probably mildew or some other rain impurity left in your phone.
Hope this helps.