Try these simple steps and check if this makes any difference:
1. Remove AC Adapter and battery from the computer.
2. Remove any External peripherals from the machine.
3. Press and hold the power button for 10-15 seconds.
4. Re-connect the AC Adapter only and try to power on the computer.
5. Check if any difference is observed.
6. Now check the Video on external Monitor.
7. If video is displayed on the external monitor and no video on the Notebook LCD, this indicates an issue with the Notebook LCD or the LCD cable.
8. Take a technician's help and try to reseat the LCD Cable. Refer to the Service Manual for detailed steps on how to reseat the LCD Cable.
9. If the Video is not available on external monitor as well this indicates a failure with the Video Chip on the motherboard.
Note: Some of the steps above require you to reseat the components by removing the system cover/taking apart the chassis. Please perform these steps only if you are comfortable else seek a technician's help. Also, refer to the Service Manual for accurate steps and safety instructions.