As caf4926 noted, your PC has:
00:14.2 Audio device [0403]: Advanced Micro Devices [AMD] Hudson Azalia Controller [1022:780d] (rev 01)
Subsystem: Micro-Star International Co., Ltd. Device [1462:d696]
Kernel driver in use: snd_hda_intel
which appears to be your audio device.
and like caf4926, I don’t know the importance of this:
02:05.0 Multimedia video controller [0400]: Conexant Systems, Inc. CX23418 Single-Chip MPEG-2 Encoder with Integrated Analog Video/Broadcast Audio Decoder [14f1:5b7a]
Subsystem: Hauppauge computer works Inc. Device [0070:7400]
Kernel driver in use: cx18
although the cx18 driver supports the cx23418 chip which is for IVTV and multimedia capturing. You ‘might’ be seeing that in YaST hardware-sound, but I don’t think so.
I also note this for your Video
00:01.0 VGA compatible controller [0300]: ATI Technologies Inc Device [1002:9640]
Subsystem: Micro-Star International Co., Ltd. Device [1462:7696]
Kernel driver in use: fglrx_pci
where I note the 1002:9650 PCI-e device corresponds to a AMD HD 6550D. I also note that Radeon (AMD) graphic hardware device will often include HDMI audio.
Hence it could be that one of the ATI or AMD devices you see in YaST is your HDMI audio, which you likely are not using. And the other AMD/ATI device you see could be the device that is using the snd_hda_intel kernel audio driver.
I recommend you install the application ‘pulse audio volume control’ (pavucontrol) and run pavucontrol the 1st time you run any multimedia application and tune pulse audio to work for that application (being certain NOT to select the HDMI device, but rather select the regular audio device). I have some hints/examples on using pavucontrol here: Pulseaudio Basics for openSUSE with pavucontrol - Blogs - openSUSE Forums
Now if you still not succeed after that to get your sound working then I propose you provide more information by running a script that will give us detailed audio hardware/software information. You can do that, by running, with your PC connected to the Internet, the following command in a terminal as a regular user:
/usr/sbin/alsa-info.sh
and select the SHARE/UPLOAD option. When the script is complete, it will in the terminal give you a web/internet address where it has uploaded the audio information. Please post the web/internet address URL here so we can examine better your PCs audio configuration.