Both MacBook and external monitors go to Black screens

I used My Macbook core duo with a Dell external monitor after the LCD of my Macbook went black.

I had to tilt the Macbook screen and adjust a VGA connector between Macbook and the external monitor to mirror the macbook screen to the external monitor.

Finally, my external monitor went black.

Strangely, when I clicked at the right top of the desktop screen of my mackbook with the black screen.

For a second, the mackbook display showed a regular screen and went black immediately.

Please help me fix this problem. It borrowed this from my professor.