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?
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.