If you take the screen apart to reveal the actual panel (it's got a metal backing, it's usually right underneath the plastic of the laptop) you can then search that model number and then the word driver in eBay and find a display driver board that will take the output from the Wii and make it the right signal for the display.
For battery, you may be able to reuse the original pack if the battery life was still decent, and if not you can always buy batteries like 18650 cells (it's a type of battery, slightly bigger than a AA battery).