AUDIO OUT JACK MALFUNCTION

No way to do that unless you can figure out a way to remove the part. The contacts inside that plug determine where the sound goes. No way to turn it off unless you remove the broken part. If you feel confident enough, remove the back of the TV and remove the broken piece from the jack.

Replace the headphone socket of the TV. It has contact fault.

You will need to remove the broken piece. Power down the computer and unplug it. The only suggestion I would have is see if you get get to the jack from inside the computer and push out the broken piece with a paper clip.

Wires connected wrongly. Unsolder and switch the wires the other way round.

pull the plgu of your headset partially from the jack play around it until the other headphone produces sound if this happens it mieans that the Audio port your using is either malfunctioning or you can try youy headset with an MP3 player or any audio device that uses a headset to find out if it is the headset that is damaged

if you are not handy, then no.
repair will require disassembly of the ear piece, splicing of the wire, and reassembly.

Yes you do or if your careful you can back it out the jack with needlenose plyers.

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the diagnostic mode won't check the audio, only the headphone jack.
I suspect that the sound on your ipods motherboard went out. It happens!
Have you been using the ipod on a dock, a speaker dock, any dock?
If so the dock may have damaged the motherboard and too the sound out.
Or the sound on the board just went out. You can fix the boards without special equipment and
skill. If that has occurred, which if you replaced the headphone jack with a new one, has occurred
you are looking at replacing the motherboard in your ipod.
You can find a new motherboard on ebay for about 40.00 or so.

Good Luck

Call customer service for assistance to issue.

Most common cause is that the solder connection that holds the headphone jack to the board is broken. Usually can be fixed by taking the player apart and re-soldering the connection. Takes some effort and a pencil type soldering iron.
The T10 headphone jack is underneath the main board and you have to undo a solder connection in order to remove the board to gain access to the headphone jack. It's a lot of work but it can be done.