so you have two soundcards there, and both are run by snd_hda_intel?
your output is a little confusing, it would be better if you could show continuous lspci output for your sound hardware.

so you also have two different places on your machine to plug in cables?

in any case, i don't use pulseaudio, but on my alsa system i would open alsamixer in a terminal, press F6 and select the sound card that gives me sound.
i guess you'll have to find the equivalent of that for pulseaudio.
when that works, we'll talk about making it permanent.

lspci -v | grep audio

reports

00:14.2 Audio device: Advanced Micro Devices, Inc. [AMD/ATI] SBx00 Azalia (Intel HDA)

and module

snd_hda_intel

is loaded.

????

yes, I'm stumped
no INTEL audio card is showing up under alsa or pulse only the HDMI video card

currently I am outputting through HDMI to monitor then analog out to amplifier

assuming it is hardware
"Gigabyte Ultra durable"