You don't want to install Windows on one computer and then move the drive to another one unless they are identical. At best you will get tons of driver issues, at worse, the PC won't boot.
Since the LCD is already off, I hope you have a physical button that pushes in when the lid is closed otherwise this won't work. Plug in the monitor, turn on the laptop and hit the "lid closed" button. The laptop should detect the external monitor as the main display and send the image to that. That's assuming the laptop can even boot with the LCD disconnected, you may need to connect it again.
Are you sure the issue is with the LCD and not the video card? Is it cracked or did it just stop working? Maybe the issue is that your video card just does not output anything anymore which is why no video works, or another system problem is at fault.