I have no experience with backtrack, but I think it could be that the right module is not compiled. Do you have the kernel sources installed? If so, try to call "make menuconfig" in /usr/src/linux and check if Device Drivers -> Sound -> ALSA -> PCI Devices -> Intel HD Audio is selected as a module. I think that this is your soundcard. I have this one as well, lsmod says, that the module snd_hda_intel is loaded ad boot time. Does your system load it, too? Do you have this in your lsmod?
00:1b.0 Audio device: Intel Corporation 82801H (ICH8 Family) HD Audio Controller (rev 03)