I have a 40" TCL TV with one black vertical line on the screen.
Your set has some board that performs the function to connect the screen to the video-generation function of the TV. Either your LED/LCD screen is failing or the video function is failing. If the set is under warranty, contact the manufacturer using the information on the warranty statement. Try using a different video input (hdmi/composite/etc) for the TV and see if you get the same line on all inputs. If there is no separate board, the next step would be to try and replace the main video board. With the prices falling on lower resolution TV's, it would probably be cheaper to replace the TV than trying a repair, if it is out of warranty. 40" 1080p TV's can be had for less than $200 at some sales (e.g. Black Friday).