IMO an excellent piece of trouble shooting 
I am not familiar with ASUS bios, but I would look in there for a way to stop your optical drive from booting at system start up.
I think you will still have kernel problems in the future and since that long command did not work as expected it will be necessary to manually clean your system.
Your sources look good. Are you aware of the change for AMD drivers between 14.04 and 16.04?
If it was me, I would not be happy with just repairing this. I would instead opt for a fresh install.
Whats your thoughts?
PS
To use code tags highlight the code and then click on...
