Let me tell you how to deal with sound card problem as I know.
I will show you my computer's configure as example.
1. lspci and you will see your sound card config info, mine is :
0000:00:1f.5 Multimedia audio controller: Intel Corp. 82801CA/CAM AC'97 Audio Controller (rev 02)
you will find a string like "0000:00:1f.5"
2. lspci -n and get the string contail info like "0000:00:1f.5"(you have your own)
0000:00:1f.5 0401: 8086:2485 (rev 02)
also, you will get "8086:2485"(of course, you will have your own)
3. less /lib/modules/`uname -r`/modules.pcimap and you will see a lot of info about all kinds of modules.
please pay attention to the info of "0x00008086 0x00002485"(you just have your own), and you will find the module
you should load. Mine is "snd-intel8x0"
4. modprobe it. Of course you should remove all sound card driver first.
5. You can also try to check whether kernel contain this module, find it in /lib/modules/`uname -r`/. If you can find the name in modules.pcimap, kernel contains this module as usual.
If you don' find certain module, that means alsa don't support your sound card. You may try to reinstall your alsa
If you can't read sound card info(vendid, etc), it means kernel don't know it.
All above is my experience, share with you and best wishes.