Maybe I'm not understanding your description of what is going on, but are you saying the top half of the screen is fully lit and has an image, while the bottom half of the screen is black? Sounds like a damaged screen to me. The inverter and inverter cable generally either work 100% or they don't work at all, and I've never seen a situation where they only succeeded in lighting half the screen, and the inverter or cable was at fault. If light is getting to the screen, and half the screen appears dead, it's probably a screen issue. Is the dead half of the screen 100% black with no image, or is it just faint, and you see a faint image?
Yes, if you have a replacement screen to test with, then by all means swap that out before even thinking of replacing cables (which involves opening up the hinge, which you don't want to do if you don't have to). For instructions on replacing the LCD panel, take a look at this video tutorial on my site: