Obviously I looked in the wrong places, and the solution is pretty easy, which I only now had time to fix. This sound card is reported as Intel Corporation 5 Series/3400 Series Chipset High Definition Audio (rev 05) and its required modules have been moved to a separate package. To get support for it is just a matter of:
apt-get install linux-backports-modules-alsa-2.6.32-23-generic
In fact, I really love this laptop. The only thing I dislike, well, *hate* is the keyboard. Someone at HP Labs wasn't very smart, since they added a left column of (unusefull) "multimedia" keys right next to the standard layout. So, while you're not used to it (which happens a lot when you switch between multiple computers all the time), you keep launching the calculator, printer spooler or even the e-mail client, just to name a few. As a matter of fact, it seems HP made everything so well that they couldn't sell perfection so cheap. It's obvious the layout designer doesn't use a keyboard at all :-)