After some more research, I think I've found the answer to my own question. Anyone else can feel free to verify or refute my claim.
I have found two instances ([http://forums.ilounge.com/showthread.php?t=227875|here] and [http://www.mcelhearn.com/2007/07/16/what-to-do-with-a-dead-ipod/#comment-1378|here]) of iPods not getting recognized by a computer due to lack of a battery. Therefore I conclude that iPods, unlike every other battery-powered device out there, requires a battery for proper function despite the fact that a charging cable is present.
That means my iPod's simply suffering from a dead battery. And because I've already fully disassembled my iPod, and Nano batteries are dirt cheap, I think I will be doing a battery replacement. Problem solved?