This assumes the following : 1) the line is sharp 2) the line never moves 3) the line is always there.
The short answer is, “it is in the display electronics driving the flat panel array”. This means it is irreparable “in the field”. Meaning anywhere but factory.
The long answer is to explain the workings of the display drive electronics, but the net answer is the same…....
It is possible that the problem will only occur at certain temperatures or other specific conditions, but the net answer is also the same.
If this is under warranty, it will be a new TV, since the panel will not be a shop replaceable item.
Since you say the line is on the right hand side and goes away then it is not the panel electronics, but more likely in the video that you are feeding it. if there is not enough information, or picture to fill the entire width of the screen, the vacant signal area could be anything, not uncommon to see green.
If the HDMI cable is really the problem it could be affecting the signal in timing, lots of this kind of thing can be seen on computer monitors with longer vga cables, the length of the cable causes signal degredation and image blurring, as well as lines of this type. Since the sync signal is often embedded in the green color signal it is most likely this color you will see.
the component signals are much easier to send longer distances thru cable, because of the design impedance of the component system – so they are less likely to have a cable length problem. I might suggest a high grade HDMI cable; there are cheaper cables which could cause this problem too. For the sake of signal, this can be the weakest link so its best to spend a good coin on it.
Hope this has covered most of the bases for you.
Good Luck.