Laptop screens have used a digital interface for years. the cables may not look like a standard DVI connector but all the cables should be there. It is also likly to have some extra leads for power signals.
I think you would have to buy a blank DVI conector and work out the cables. As for the backlight if you are lucky then inside the TFT besel will be an inverter board, this will be have two (probably?) cables going into it from the laptop measure the voltage and match.
In short I would not consider this unless you you have and can use a soldering iron, ociliscope and lots of time.
However if you do get this to work then post the results for us all to see. Oh, one more thing, Good luck!
Only the insane prosper.
Only those who prosper can judge what is sane.