This issue is easiest to repair by just replacing the screen like DanJ mentioned - but its technical name is "dustgate" (not to be mixed with flexgate) You can repair this by replacing the data flex cables on the screen, as they get punctured by dirt and dust over time. It is a very complicated and delicate repair, but some repair shops do offer it.
Here is a close up of what can cause this damage to the cables.
I was actually just working on one today and have a few pictures to share of what needs to be done.
You need to remove the Panel from the housing,
Then, you need to un-solder the flex cables so you can solder new ones on - they will go from the tcon board to the screen. I didnt finish the work today, so this is all the images I have.
Not something that is really a DIY project, but - a shop might want to buy your screen, or offer to fix it for you at a better price than a replacement would be!
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