Use your iPhone in bright light, sunlight will work, can you see a faint image on the screen of your iPhone working? If yes, you have "No Backlight Problem". This can be fixed if LCD Display problem by new LCD Display. If Logic Board problem often a Coil of the several Display chips can be replaced by soldering.
If the screen is just completly black:
Best possible senario, LCD Display Flex Cable #1 came loose from the Logic Board, doubtful because it was in your hands but you never know. Genius at my Apple Store will push this #1 connector down for free. Make appointment with Genius and ask them to reseat Flex Cable #1 to the Logic Board for you. Before opening and during repair on iPhone 3GS make sure the iPhone is OFF or you risk further damage to it.
Next senario, LCD Display is faulty. Replace LCD Display.
Worst senario, Logic Board Display controllers are damaged.