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 (here and 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?
Just to clarify, the parts would only be different in models with 16GB or memory or higher. The 8GB model remains identical between the 2G and 3G except for a price drop.
Unfortunately, upgrading the graphics on your model is most likely impossible. The HD 3200 is a graphics chip that is directly soldered onto the motherboard rather than a card, which may have a chance of being removable. But even if it had been a removable graphics card, chances are slim that you could find something else compatible with your existing motherboard and fits the voltage/temperature/size requirements of your tablet PC. Fortunately for you, the HD 3200 is very good for an integrated graphics chip. My 15-inch Dell is many times more massive than your 12-inch tablet and has a nVidia GeForce 8400 GS card, but benchmarks show that your 3200 is only slightly slower than the 8400.