The LVDS cable is the video cable that carry the video signal from the logic board to the LCD panel via 2 connectors. Dark shadows can be caused by a defective backlight lamp if the shadows are starting at the screen base or by pressure points on the screen (applying excessive pressure in the screen with the fingers, etc). In the two cases the LCD panel must be replaced.
Concerning the varsityanchor lines issue, that's bad news if you get no video on the external monitor. Most of the time that leads to a defective logic board since the early MacBook Pros had problems with the Nvidia 8600 and the Ati 1600 GPUs. But you should get an image on the external if you have one (even with lines) on the internal. Are you sure the external monitor is well connected ?