Need Help - Black screen in Dell Studio 1555

My Dell studio is not booting. When I press power button, screen remains completely black all the time (BIOS screen does not appear too). Once in a month or two, it suddenly starts and function properly but after shutdown and restart black screen appears again. Following are some of the symptoms I noted.

1) No beep sound

2) Once I press power button, my keyboard lights up. Power switch lights up too. I can hear the sound of fan etc.

3) I have tested with an external monitor. Display appears there. So assuming my graphics card is OK.

4) Pressed 'D' and powered on. Colors are shown properly on LCD panel. So assuming my LCD panel is OK too.

5) Pressed 'Fn' button and powered on. Screen remains black.

6) Once in a while when it starts (or when I connect it with external monitor), I see a few Red and Green vertical lines on screen which gets cleared once windows login screen appears.

Can anyone please suggest what could be the problem? My laptop is out of warranty.

Thanks