I had a similar problem with HP 630 laptop. I can't check if it had the same sound card, but I did spend some time with that (as you probably have too) and found various solutions, though I didn't test all of them. Here are some, for example:
However, this solution worked for me (instructions are in German, but you can read the commands)
In short, install Linux-Alsa-Driver-Module from ubuntu-audio-dev/ppa:
$ sudo add-apt-repository ppa:ubuntu-audio-dev/ppa
$ sudo apt-get update
$ sudo apt-get install linux-alsa-driver-modules-$(uname -r)
I can't promise it works for you, of course.