You have to determine if the problem is the output of the TV or the transmitter for the headphones. Connect the transmitter to another source (your phone for instance) and check the function.
If it doesn't work then it is your problem.
If it works then the TV optical may not be working or the DAC is bad.
Since you have been in the TV menu I assume that you followed instructions on using the optical audio out.
If you have a VOM you can check that the power supply for the DAC is OK.
Check the DAC on another source with optical out (another TV, DVD or CD player).