only think I could suggest it to remove the LCD connectors from the laptop and give it a clean, if everything else seems to be working fine. this might be the issue. you have not mentioned the brand of the computer since I'm using an HP this is how Ive removed my LCD I work on hp laptops but most are the same orientation as far as assembly and removal. There are many rubber pads that you will have to peel off that will reveal screws on the front of the lcd bezel assembly. After removing those screws carefully pry open the bezel the plastic part around the lcd screen. It might be a little difficult because there is tape there to keep the bezel from having gaps. Just try to find an area that is poped up a bit and start there. After the bezel is removed, look on the side of the lcd panel assembly. There will be a couple of plastic screw covers that you will have to pop out from the inside of the lcd panel pushing outwards. Then remove the screw there and the rest is self explanatory as there will be a lcd bracket on both sides of the lcd panel, once you remove this you should be able to see the connector cable.
However I suggest you should take it to some one who have done this before depending on the manufacturer methods of getting in to the LCD connector might differ.
good luck !