Sorry I can't find a service manual for your laptop.
I assume that you tried pressing the "special" key on the laptop which turns the screen's backlight on and off. (see image - taken from the NV77H User guide - see link)
Here are a couple of You Tube videos showing the dis-assembly of your laptop and the replacement of the screen. Hopefully they may be of some help.
Just a stupid guess on my part, but I'm wondering, since the backlighting can be controlled by pressing a key (see above image) then perhaps it is software controlled. It still needs to be aware of the lid position though. After looking at the videos and "Googling" the part for a closer view I'm thinking that the lid switch might be part of the Power Button board assembly. It is in the right position (back right corner of the laptop) The board seems to have more wires on it than just a couple needed for a 'press to start' function. Again this is just a very wild guess on my part.
Sorry I cannot be of more help.
Here is a bit more information I added to this great answer. Your logic board should be a Compal LA-6911. If you look at the board carefully you should see it silkscreened on it. Let us know if this is correct or if you have a different board. There are multiple variations. The schematic does not include a board layout, so you depend on the reference designators on the board itself. Not easy but possible.
Thanks jayeff for letting me add to it ;-)