This card seems to be a bit problematic
One solution I see is (but possibly to old a solution)
The SiS7012 sound card will work by removing Alsa modules and enabling the corresponding DSP driver (i810_audio). You need to configure XMMS to use the DSP (in XMMS options).
Now don't cry if you don't get it - this is the last resort and I'll help you with it you need to go there
From your post I get
card 0: SI7012 [SiS SI7012], device 0: Intel ICH [SiS SI7012]
ICH means that it is Intel HDA and it is very probable that the standard solution
for all kinds of problems with HDA works
You change model to what ever you have or auto or some more exotic model like in this topic
You may have to try many different "models" to get it to work - brand or model ...
Note the link to a post in the Ubuntu forums for a list of "models"