Your built-in HDA Intel sound card consists of a "controller" part and a "codec" part. If you have a new controller, the default driver usually works okay.
If your codec is not supported, however, you're very likely to run into problems such as one or more inputs/outputs not working, headphones not muting internal speakers, etc.
To check if your codec is supported, run this command:
grep "Codec:" /proc/asound/card*/codec*
You will get one or more lines of output, perhaps something like this:
/proc/asound/card0/codec#0:Codec: Realtek ID 662 /proc/asound/card2/codec#0:Codec: ATI R6xx HDMI
Now pay attention to the format of the output: If a row is in the "<vendor> <chipname>" format, it is supported. If it is in the "<vendor> ID <number>" format, it is not supported. In the above example, "ATI R6xx HDMI" is a supported codec, whereas "Realtek ID 662" is not supported. If it is not supported, and upgrading your sound drivers does not help, somebody needs to write a kernel patch for this hardware to be supported.