I read on the AMD website that the proprietary drivers for many of their sound and video hardware will not be updated to run under the newer kernel used by mint 14, but they are still supporting the drivers that run under the kernel that is used in mint 13, so if all other options fail you could consider going to it. With that said, please try the info below, it works for me.
Have you tried looking for the sound device control interface? On 13 it can be easily found by clicking menu, then pointing to system tools, followed by clicking system settings, where I can then find an icon for sound, this is likely the same for 14. Once there I find the following interface:
Notice the on/off toggle, make sure it's on, and that the HDMI device is highlighted. Connector needs to be set to "HDMI/DisplayPort".
In the Hardware tab your version of HDMI Audio should be highlighted.
Also the "Profile" at the bottom of the window should be set to something saying HDMI, and not to off.
I find the other 3 tabs unimportant to running sound out through my TV speakers.
I'm not saying that this will cure your problem, but it is a place to look.