What does green screen on 3gs mean?
You could try connecting it to a PC or Mac and use iTunes to restore the device. It's not likely software is causing this, but you will know if the rest of the phone works and possibly fix it without needing to take it in for hardware service if the display function is broken.

You won't be able to tell if it's the screen or the cable or the video subsystem without replacing parts or getting into the hardware to at least reseat the cables but this is most likely a hardware failure.