You will need to use a controller card to use that laptop screen. Those can be expensive.
If you are trying to keep this system cheap, I suggest you find a different monitor. There are tons of laptop monitors out there for cheap, and the reason is, its not easy to make them work with a regular PC. However if you find the correct controller card it will work.
Another thing, why such a large computer. Large not meaning speed and such, but size?? That computer case is HUGE. Do you plan on using that case or taking out the parts and integrating it into your car?
My 2 cents