Bob,
I suggest experimenting with a couple of things in the audio portion of the TV setup menu. I'm referring the manual at:
http://elementelectronics.com/Manuals/FLX-1910_manual.pdf
This should have come with your TV. The audio portion starts on page 32. First, make sure that you are using the TV as the source (and not a DVD player or other). Keep the coax connected to your RCA system, have the RCA system on and set to the correct input (DVD is what I think you said), and then try these things.
1. Set the "Speaker" option to "Off". Perhaps it won't output through the coax if the speaker is set to "On".
2. If that doesn't work, try setting the "SPDIF Type" to either "PCM" or "Dolby Digital" to see if one or the other works.
I find it curious that the manual specifically recommends against using the TV audio out (i.e. coax) port, even though I'd think that would be the only way to output sound from the TV itself. It may have be just a poorly written paragraph, and I know that they are trying to recommend against routing all of your audio (from your DVD player, satellite receiver, etc.) through the TV.
If that doesn't work, I'd recommend contacting the TV manufacturer. Also, just FYI, a few user reviews of your RCA system on cnet.com mentioned that the system is unacceptably quiet. Perhaps it's the RCA.
Adam