If you have some idea about the working of your TV, and some service experience you can do it by yourself. Your TV has electronic volume controls. That means, a gradual voltage rise or lower does the volume to go up or down. This voltage variation is done by an Ic which we call it as "System Control Ic", that every modern TV has; but differ in their type and number. You must know how to follow the schematic diagram of your tv to get the exact point from which the voltage orginates, and which point regulates the same.
At present there is some voltage, say 0.23VDC or so, remains at that control point even if you turned all the visual controls seem to be off; and that voltage suddenly goes up; say 3.05VDC or so when you adjust the volume to the near mid stage. Further saying 3.05VDC must come only after you have turned the volume bar to extreme high. Now you are listning your tv at is 1/4th volume at extreme low I thinks.
Looking for fault at system contol section must be done with patience, and should have schematic diagram of it, and some sort of skill. It is best for you to get service of an experienced service personal, otherwise the the faults will be rise in numbers. All sony tv has complex schematics even go to pages on a book, and have some difficut to follow even an experienced one you know. So think a little better and do the needy.
If you have confidence that you can reach the the above said points, contact me at my mail address which is given below. I will guide you. You must have the schematic digram of your tv also beside you. Ok.