We had a similar problem with the thin blue vertical line at the right side of the screen. We have the same TV too, the UN60ES7500. It started happening a few months after purchase. I was also skeptical of Samsung products but I really liked the screen of this TV (especially in Dynamic mode). Out of all the TV’s and most electronic products I’ve owned, I’ve never had to use the actual warranty to get something fixed. My view is that if it breaks down that early, then there was something wrong with it to begin with. And thus, I’ve avoided brand names that I’ve experienced this with (Samsung being one of them).
For me an average TV lasts about 10 years without any servicing (that’s how long I’m used to things lasting, so I thought this was a joke). Anyway, I used Samsung’s customer support page which was pretty intuitive. It gives you options to upload photos or a video of what the problem is. The technician called me the next day to say he was waiting for the necessary parts from Samsung and that he'd call when he gets them. He called only a few days later saying he got the parts & that he could come that same day. So I was already impressed by the speed. (By the way, I found out later that these warranty technicians are 3rd parties hired by Samsung, they don’t work directly for Samsung so the quality of your service can vary). He brought what looked to be like a brand new 60” TV but it really wasn’t - it was just the screen panel he was going to be replacing. It was so big I had to help him bring it up our apartment. After he finished replacing the screen, the TV would only intermittently turn on. So he at first thought it could be my main board and he exchanged that with one that he brought. After doing that the TV wouldn’t even turn on at all! So the 2 Samsung parts that he had brought with him (a 60” LED screen and a main circuit board) were both apparently defective as well! It was unbelievable! The technician was surprised as well and started giving me a little more credibility when I told him of my bad experiences with other Samsung products. It’s not his fault though, he was good and most importantly he knew what he was doing (which unfortunately doesn’t always come with the package these days in tech support).
We were about to call it quits and just put back my original screen and main board and have him order the parts again (I could live with the vertical blue line but not the TV not powering up). Before we did that he wanted to try one last thing. In the back of the screen there's what’s called a converter board.
It’s the green colored thing in this pic of the screen (yes, the rest of that is the 60" screen he brought with him to replace). He took that converter board out of the screen and replaced it with the one that was in my original screen. And guess what? It worked. It was kind of like the 3 Stooges method, switching & swapping parts of my original TV with parts that he had brought with him and in the end we got it to work. For how long will it stay working? That can be anyone’s guess but I’m hoping it lasts at least a few years (my expectations have gone down significantly now that this has happened and because of my previous experiences with Samsung products).
Luckily this was under warranty, otherwise it would have costed $900+ (I saw a tag on the replacement screen with the price). So for the original poster who’s had his TV for 6 years, this is your solution but it isn’t a cheap one. The other option is to get a new TV.