I was unable to get anything to work (but I understood what the issue was by following the steps in the write up), then I come across the section titled: Getting the ALSA drivers from a *fresh* kernel.
I performed the following commands to freshen up my ALSA drivers.
sudo apt-get --purge remove linux-sound-base alsa-base alsa-utils
sudo apt-get install linux-sound-base alsa-base alsa-utils
sudo apt-get install gdm ubuntu-desktop
After running aplay -l and subsequently seeing that my drivers looked secured, I head back to The Casters YouTube video on Terminal and Initial Objects that I want to watch and was happy to listen to audio again! Thank you LordRaiden!