Hi AND EH,
What is the exact system model? Does the system power on and stay on or does it go off automatically? Do you see any leds come on and stay on when you press the power button?
Try using a flash light and check if any dim display in visible.
Run the LCD bist - Turn off the system and press and hold the "D" key + power button to turn on the system and it should run the LCD built in self test - see this link for more info - http://dell.to/1SkXNrG
While running the lcd test and the diags - swivel the lcd back and forth and see if the display comes on.
Also, try the onboard diags - press and hold the fn key + power button to turn on the system and it should initiate the diagnostics - check if any beeps are heard. This will help isolate the source of the issue.
Connect an external monitor and check if the display is seen.
Write me a private conversation with the service tag and your contact details(Name and Email) for case records.
If there is no warranty, then you could contact our team to get a quote for a paid service call - http://dell.to/1vnT6CQ
Let us know if you have any other queries.