LCD cable short circuit

Well hello,
a few days ago I stumbled on my own feet and my laptop slipped out of my hands, breaking the hinges. until I will get new parts, I decided to still use it. today, while watching a movie, the lid curved back a little, leaving me with a white screen. adjusting the lid back fixed the problem, although it happened everal more times, with either white or blavk screen. later, forgetting the hinge issue I laid it down on the table, when it seemed to crash and shut itself down. after turning it on again I saw a flash where the lcd cable goes and smelled something burning.
now, the screen is black, when turned on the vent starts in about 10seconds and after 29-30 seconds it shuts down again. the cable also obviously looks burnt.
so, the questions are:
can I fix the cable?
would replacing it help?
could the short circuit have damaged other hardware?
is it even a cable issue that makes the shutdowns appear?

I have a dell latitude e4300
and I would love the one helping me out till I die

Have you got an external monitor/tv to plug it into to test?

Yeah, we tried. it said no signal.
what worries me is the instant shutdown. can I try else?

JUST TO CLARIFY-
ventilation starts working in about then seconds after hitting the power button and in about twenty more seconds the laptop shuts down without a warning/there are no beeps to follow.

You have fried the motherboard... Is it time for a new laptop? The repair cost on this may be way too high