You could always download vnc onto both laptops.
Such a useful piece of software that I keep it on my webspace.
www.mlweb.co.uk/software/
Make sure you add a good password though especially if your not behind a router.
You'll need to connect it to a normal computer screen to install it but after that you can fire up both machines, use vnc to connect to the one with the busted screen and put vnc into full screen, it will be 100% what your looking for.