Hello
Picture being Ok, and no sound output, means there is some problem inside the sound output circuit of your TV. It may be due to a speaker fault or an IC fault. You have to find out which of these has fault.
You just place your ear very close to the speaker side, and switch on your TV with its AC mains On-Off switch, not by remote control handset. Listen carefully, whether there is any sound output of any form comes out of it or not. If there is no sound at all you can determine that the speaker may be out, not in all cases. If you have the habit of listening your TVs audio by using a headphone, continious in-out action could damage your TVs headphone socket. If the headphone sockets' contact got damaged, no sound output will come from it to the speakers. Suppose you can hear the sound through your headphones but not throuhg speaker, means that its change over contact has some trouble. You just do this first. Insert a headphone pin into your TVs headphone socket, if provided, al listen to it for sound. If there is no sound from headphone also, Sound output Ic iside your TV has damaged, or not getting proper voltage to it. If there is sound through the headphone, and not from TVs speaker, trouble is related either speaker or the above said socket.
If all the above has no effect, that is no sound either from headphone, of from the speaker, you should go into the circuit board of your tv to get the fault.
Open your TVs back cover, and trace for the sound output section. There will be an Ic used as sound output. Check whether it getting heated some time after switch on the TV. If it overheats without any sound output, it is damaged Desolder it out from the circuit board, go for a same type and number, replacing it will solve the problem. If it doesn't overheat, or no heat at all, check its input voltage. In some cases, loose soldering points on the legs of Ic may also the cause. Check it too. Ok.
If you need any more clarification, ask me through Fixya. Give
a brief explanation about what you have done so far also.