You would need an LVDS to VGA converter to adapt your Laptop display to accept a VGA signal. Like
this one.but not all laptop LCD display's are the same so you would need to make sure the above adapter will connect to your (1 of a billion different types of) monitor.
Then, you would need a VGA to ypbpr converter to convert the Xbox HD signal to VGA. Like
this one.This is the main reason (next to power constraints) why no one has build an xbox laptop. Try cramming all of that stuff into a laptop shell.

Trust me, the screen from a dead laptop is useless. I used to hang on to them too until I found out that they are really only good for replacement parts for another laptop so unless you have tons of money and time (and are trying to connect one to anything but an xbox), or are a laptop repair guy, there is no reason to save them.