By the look of it I`m afraid that what your tv has is another case of defective LED strips and this is very common with the LN serie of LG tv`s .
Those LED`s are supposed to last a zillion hours but they do not , they are failing all over the place and not only in LG
Here is a link to give you an idea what is needed ;
Mind you they don`t have it in stock at this time , these guys can`t keep up with the demand but if you were to look into this yourself then you could sign up there to be notified when back in stock .
It usually takes less than a week but before you order I must say that this is quite tricky to perform , the lcd panel has to come apart to reach those led`s and unless you are very handy working with electronics , I would not recommend it.
To have this repaired at home could cost you around $250 parts included and perhaps $50 less if you take it to the shop yourself .
If you need to find repair shops near you then look at the link below and enter your zip code ;
This will give you a list of NESDA member repair shops in your area.
This list may be limited though and you may find more by simply using the yellow pages or simply google "tv repairs" and the name of your town .
You could give a call to different shops in your area to get an idea of their rates , it pays to shop around .
Let me know if you have other questions and if not then please do not forget to rate by clicking on the star icons at the top, then click on Submit so i get paid for my time helping you .
Also note that it will not close this post , you can come back here at any time if you need further info or help .