On my desktop, Clementine throws this error and I do not hear any sound.
VLC is able to play fine.
How do I go about researching this issue and find a solution?
I don't see your error, only your lspci output.
Just downloaded clementine and audio works ok for me with Intel sound chip.
This may help, open Clementine:
Goto tools, prefernec, playback.
The last section Gstreamer audio engine chooses which device to channer audio down.
I tried them all, and could get audio with all engines except two:
ALSA audio sink
Apple Airport Audio Sink
Change these settings, if still no audio, open a terminal, start clementine and post
the error message.