I've already tried several things here, but instead of mentioning them, I'd like to start from scratch.
I've installed alsa-lib, alsa-util, alsa-firmware, and linux-firmware.
When I run 'alsaconf', my card isn't detected. When I run a speaker-test, my card isn't detected. Keep in mind this is an older card, obviously. I had to compile the firmware myself in the latest Debian testing to get it to work.