Thank you for the very clear description of the problem.
The symptom you describe is consistent with a possible failure of the inverter board.this is the board that provides the high voltage to the backlight lamps.
It is basically and oscillator circuit married with some step up transformers.Something in this oscillator circuit it starts to fail=high pitching noise from the transformers.
Now this is not an immediate sign of failure of the tv set,but eventually it will fail in the future.
The fix would be to replace this inverter board.The board itself costs up to $100,but Samsung is not providing it as a separate part,only with the LCD panel together(to replace the panel will be way to expensive,exceeding cost of the unit).
You still may find an inverter board,but I need to know what is the unit's complete model code,version(VER#) and serial#.These will help me identify the right part#,since under the same model# XXXXX many versions,using different panels and inverters.
If you want me to research this part for you ,please provide the above info.
If you do not plan to replace this part by yourself,then,the estimate to repair this unit will be "the part cost"+ about $100 to $150 for labor fee.
I hope this help,let me know if you need help with the inverter part#.
Thank you and have a great day!