my powerbook g4 screen does not work

I have a powerBook G4 with 512 ram 800 mhz and a 30 gig hard drive. The computer will boot perfectly fine (fan will go on and you can hear the start up chime) but the screen will not show. The computer has been damaged( see below). I did get the screen to work once though the screen only lasted ten minutes before i went blank again. I would like to be able to connect it to an external display but when I do nothing happens for both dvi, s-video, and VGA (I have a dvi to VGA converter). Can anyone help me?