>>2010793
you'll need to use the external video output connection on the working laptop (I'm assuming HDMI) to a converter/driver board for the extra LCD.
Laptop LCD's 99.99% of the time use "LVDS" interface, or Low Voltage Differential Signal. So you'll need to get an "HDMI to LVDS" driver board. What laptop are you ripping apart? You'll need to find a part number on the LCD so you can find the proper LVDS driver board. >>2010840 is the correct type of board you're looking for, but it may not be for your LCD specifically.
You will also need to make sure you have power for the external LCD. Most LVDS connections for LCDs will supply the power along with the signals for the image all in one cable. However, there is a chance that you'll need extra power cables in case it doesn't. We can get to that point if necessary.
What you'll end up doing is ripping out the bare LCD, getting the correct HDMI to LVDS driver board, and constructing a case to your liking. You'll connect an HDMI cable between the good laptop and the new driver board. You will also need to supply power to the driver board, similar to you plugging in the laptop to work. You can use batteries for portability, but that's further down the line. A power supply for the board will most likely be a cellphone-like charger that you plug into the wall, then the HDMI-to-LVDS board to function. The exact voltage and power rating will depend on the LCD screen and driver board itself.
At this point, you've pretty much made a basic monitor. Touchscreen will be trial-and-error. Depending on the touch interface (probably usb), you'll connect it directly to the main laptop via usb cable, and have to use software within the PC to calibrate it to function on that screen. If you were to plug the touch screen directly into the host laptop, it would act like a huge mouse touchpad and control the mouse on the laptops main screen.