Ok, it looks like one of the three things to me...
1.) It looks like one of the LCD/LED light blubs on the edge of the screen is failing/defective.
2.) The port in which your media device is plugged into could be defective as well.
3) Some TVs have defective capacitiors that leak or blow before their time,
THINGS TO TRY....
1) Try another input port. If you are using HDMI port 1, then try HDMI port 2,3 and so on. See if the problem persists. If it persists, no matter what port you plug into, then it is more likly issue number 1, that I listed above or issue 3.
2) Take off the back panel of the TV (When it is unplugged from port) and look for any "Goo" or odd leakage on the circuit board or burned spots. If you are not comfotable with this, then do not try it. Take a picture if you can
3) You could always call the manufactor of the TV and have them look at it, but I assume you posted, because you wanted to see if you could try a few things before doing that.