Since you say you can see on an external monitor.... Check the display itself, shine a flashlight on it at different angles, and see if you can see a faint view of your desktop. If no, you should then look inside to make sure that the ribbon cable that connects it isn't loose, dislodged, damaged, bent, pinched, etc.
If none of this helps, you may well just need a new display.
NOTE: If this laptop is still under warranty, do not do any work on it inside, don't open it up, and contact the manufacturer about a repair or replacement.