Hi,
Just to clarify, both setups are identical. Asus desktop computer connected to a TV via HDMI and both TVs have sound from their internal speakers. The external speakers are connected to the TV via optical SPDIF cable. One set of speakers has sound, but the other doesn't.
1. My Samsung TV sound menu has a speaker setting to set internal or external speaker output - does yours?
2. Swap the working optical cable with the suspect one (and vice-versa) to eliminate a duff optical cable.
3. Swap the speakers too if the above makes no difference.
4. If none of the above help, you could use a not ideal workaround with a stereo jack plug to the speaker RCA sockets directly from the computer.
Hope it helps...