After doing everything under the sun, here is what has worked for me.
I take the iPod out of it's dock when the computer starts up or restarts. Once booted with my iPhone attached, there is no error when iTunes starts up. I then stick the iPod back into it's docking device on my desk that is wired to my computer, iTunes continues to stay open, but I don't get the error. I can sink the iPod, and the iPhone, without the error message that my computer is not authorized.
I am attempting to restore and reinstall music on the iPod in question, and if it works, I will post it here if the problem returns or if the above workaround is still necessary.