If the old LCD cable was burnt, the LCD connector will need to be replaced since it burns the inside. The bottom few pins look a bit strange, but it doesn't look bad (difficult to tell from the picture).
Shine a bright light onto the screen itself, not through the Apple logo. Retina's are quite difficult to tell if it is no picture or no backlight (there are more backlight layers on the Retina's, so the light through the logo tends not to shine through well). Shine a light directly/resting on the screen and you should see an image hopefully, or hold the screen under a bright lamp.
The backlight fuse will likely have blown too on this model, so check continuity on that.
It's possible the original screen got liquid damage on the screen PCB (if it was spilt onto the screen) which will burn the connector here as well. You can remove the hinge cover and wifi antenna on this easily, without having to remove the LCD panel to check this. If it is burnt, replace it before connecting it to the logic board, it will blow the fuse if powered on.
Soldering is not difficult if you have the right tools, but if you have never done it before I would recommend sending it somewhere to diagnose properly.
EDIT: looking at the close up of the LCD connector, you will need to replace this. It has been burnt in this area so it is likely the fuse will blow again if this isn't replaced, or it could burn out a new cable. Replacing is the safest option, and drag soldering is your friend :)