I have been struggling with a similar problem all day. NOTHING worked, and the symptoms were like many of those in other messages in this thread. I did finally get this working, and what follows is what I did.
1. I am using a Macbook Pro, and also the mini-display to HDMI cable adapter (that is, the cable adapter is connected to an HDMI cable which then is what gets plugged in to the TV). For audio I have a audio cable ending in 2 RCA plugs (red-white) running from the earphone jack of the MBP into two audio input ports on the back of the HDTV.
2. Eventually I gave up, and turned everything off, and unplugged the cables. I shut down. I turned off the TV.
3. Plugged in the HDMI adapter with the HDMI cable to HDMI #1 on the TV (in my case that is on the rear of the TV) and plugged in the two (red/white) RCA plugs into the input ports nearest the HDMI #1 port. (no cables in the MBP at this point)
4. I turned the TV back on.
5. Started up the Macbook Pro
6. Plugged in the free end of the mini-display to HDMI cable to the MBP (the HDTV already had the plug inserted in port #1 at its end, as above). ( I did NOT connect the audio plug at this time).
7. I went and looked at the MBP display options and opened a window for each of the HDTV and the MBP displays. I could see the MBP display characteristics and those of the HDTV. [note: this might not really be necessary since you've probably already seen that the MBP is recognizing the two displays] I did it more out of trying to see what the MBP was doing, since the display itself had been blinking on and off at various times in other attempts.
8. I mirrored the displays.
9. Next I Scrolled through the TV's HDTV input options and selected the HDMI port for my input (#1 in my case).
10. Video came on almost immediately -- as I had expected when I first started hours ago. ( I've been led to believe that this is how it should have worked at the outset, but ...)
11. I then plugged in the audio cable to the MBP earphone port and then got my sound too.
Until that point I had consistently had both audio and video plugs inserted for output from the MBP. But, for some reason (in what would have been my final attempt for today) using only the HDMI video cables worked to produce a picture on the TV screen.
I don't have any technical understanding of the issues surrounding audio through the mini-display port and HDMI expecting audio in its data stream, but I wonder if in my case, the TV was 'confused' for some reason when it found no audio in the HDMI stream and yet was finding simultaneous audio input in the RCA connection. Only after the video display consistently reflected whatever the MBP was showing, did I plug in the audio cable to the headphone port. I did a test with a DVD and then a YouTube video and they all worked. The TV was happily showing the video and playing the sounds.
regards, and hope this helps in some way.