The funny thing is, the solution was simply to unplug the sound card and to plug it into a different PCI slot.

Along the way, I decided to try again to install OSSv4 (Open Sound System version 4.2). For some reason, it was smoother on Linux Mint than Ubuntu. Could not get everything to work and I found it was just better to go back to ALSA (Advanced Linux Sound Architecture). I know OSS has a simpler API and is cross-platform compatible, but ALSA seems to be better supported for my machine.

I think I may be rid of Pulseaudio for the time being, though :)