If it is working fine on the external monitor then we can safely say that your motherboard or your graphic card is not faulty. Judging that your laptop is just one year old it has got LED screen in which case we can rule out the possibility of faulty inverter. So the only thing left is to replace the Screen........but let's see what others have to say..............please post your response if it gets resolved by any means,,,,,,,,,,,,,it will be helpful for other users..........thx