Well even if the display is toast, you can access the drive.
You can either hook up an external monitor (before turning on the laptop) and then turn it on so it shows on that screen. And then access what you need.
You can also try repairing it (if no longer under warranty, as if it is still then you should contact the manufacturer) by opening it up and check the cable that connects the display and make sure neither end is loose.
Or, if none of the above works, you can remove the drive and try connecting it to another computer to get the data off the drive.