The problem is likely at the converter level. Typically this would be something that would be supported by a receiver. Even a bookshelf stereo system with optical in would probably be able to provide the connectivity you're looking for.
The other possibility, and this is a slight one, would be that the optical signal isn't working. In the back of the TV, you should see a red light emitting from the optical port.
The more probable possibility would be that the optical cord is faulty.
Without testing it, I can't determine. Sorry.