First, check the volume and mute settings, especially if there is another person in the house who may have changed them, and check another channel or input to ensure the signal source is not the problem. Next, verify that the sound is set to use the internal speakers, or that the external sound system is set to the input from the TV (some TVs with external sound output connections can be set to disable the internal speakers so they don't interfere with the external sound).
If you have no sound on any input, muting is off, and the volume indicator acts correctly, then the audio circuit on the main board is defective, or the audio power supply needs to be repaired. If your TV has a sound output connection that you have not connected, try connecting it to an external sound system and setting the TV sound to go to the external sound system. If it works, then you have narrowed the problem to the sound power amp in the TV, or to a bad power supply (some TV models have a power output specifically for the audio amplifier, although that is not common).
Most of the time, power supply failures in LCD TVs are the result of burned-out electrolytic capacitors. These are usually identifiable by the domed-up top of the capacitor, as pictured here. Note the flat tops on the good capacitors nearby. If you see these on the power supply board (the cable from the power board connector goes to the power supply), have them replaced with Panasonic FR-series capacitors; these usually have the best combination of price, power handling capacity and longevity.