Possible blown speakers

You an inline battery powered signal booster, they are cheap.

In instances of speaker damage, there may not always exist a drop-in replacement. ... Driver damage doesn't just consist of poked-in speakers, there's also blown ... You'll know if the driver began smoldering, if there's smoke to be seen on the ... Hook it up to the speaker, let it play at modest volume

What happens in a lot of these sets is the speakers are tiny--they get used long enough at fairly high volume and the paper in the speakers can tear or even come apart---if able a look inside at the speaker/s would show if this is the case.

Yes.

NEVER USE MAXIMUM VOLUME FOR TROUBLESHOOTING.
Turn the volume control to something medium.
The errant switch, control or condition may change and you will suddenly release the amp's full power and possibly destroying your speakers. If a signal isn't audible at 1/2 volume it's probably not there.

Carefully examine the front panel for clues like a misplaced Mute or Tape Monitor control or Multichannel Analog Input selected.

There is a good chance that a common control may have developed a high-resistance or 'dead' spot through idleness and is causing your symptom. Turn the POWER OFF and operate every control throughout its range a number of times, especially rarely-used ones like Tape Monitors and the Mute control.

Turn the volume to something reasonable and see if that helped.

First, make sure speakers are plugged into speaker out, not line out, and all the cable are all the way in to the ports.
Second, check the sound control in the control panel to make sure master, and other settings are up.
Third, make sure the volume on the speakers are turned up.

Some of the programs also have their own volume control, make sure those are set correct.

Thermal issue is shutting down amps till temps moderate. You must be driving your system too hard. And check out your tone control settings especially the bass. Every 3 db boost forces amp to double power at that frequency so if you are already blasting at 100 watts, a 3 db boost will compel amp to put out 200 watts, etc. Very easy to overdrive and overheat amp. You might want to try blowing air over output stages to improve cooling at high volume levels.

You are lucky that you have good protection circuits - otherwise by now you would have blown the output stages.

faulty turtle beaches i guess

Probably a short or a blown speaker. A speaker will still make noise if it is blown. Replace that speaker with a working one and see if that does the trick.

Either the potentiometer which sits behind the user knob has got a broken track or it is full of debris

You can buy a tin of Servisol switch cleaner (or similar, make sure it has a lubricant in it and that propellant does not harm plastics) take off the knob and give it a good squirt where the spindle of the potentiometer enters the cabinet

Give the spindle a few full rotations and another dose of cleaner , then give it a try

It is best if you take a cover off and apply the cleaner direct to the potentiometer

Good Day;

The TV's front panel may be bad, manual buttons. TEMPT FIX; remove speaker, cloth covered, cover, disconnect cables. TV will work but only with remote.

Good Luck!