The sound coming back while changing channel may have been a coincidence then .
With that model number I will lookup your TV's main board where the audio circuit is located and give you an idea of what sort of cost you would be looking at to bring the tv to original condition .
Without the model number I can tell you that these vizio main board cost on average 100 to $150 and if you are not to replace it yourself then you could expect a $250 to $300 bill
But there is a workaround to this and that would be a sound bar connected directly to the direct tv and dvd or even the tv itself , there is a chance that there is still sound on the TV's optical/digital port .
Beside fixing the problem it would give you a better sound than the tv speakers ,
You can buy a decent bar for $100.
Either ways you got a fix.
Let me know if you have other questions and if not then please do not forget to rate by clicking on the star icons at the top, then click on Submit so i get paid for my time helping you .
Also note that it will not close this post , you can come back here at any time if you need further info or help .