A lot of times you can "repair" the screen by heating it. I can't recall the process, but I wanna say it was taking a heat gun to the screen (after removing it from the system) and then putting it back together and the screen would work just fine.
This only works for static vertical lines shown on a GB display. It doesn't work when the GB display shows static horizontal lines or isn't working at all.
For more information on swapping the display you should search for step-by-step videos on youtube.
This one for example (although it covers the GB pocket, the process is very similar):
https://www.youtube.com/watch?v=eFBxlm6bC_UThe guy that runs this channel also has a ton of videos covering the installation of background lighting and bivert mods on the classic DMG.