As far as I know, the battery is just shot. It works, it's just that the battery doesn't hold a charge. Just looking at the battery, it seems like it's especially puffy as though it were inflated like a balloon. Luckily, the University MicroStore sold its soul to Apple and carries items like iPod batteries. I don't know what could have gone wrong with your iPod though, barqy. Sorry I can't be any more help than that.
And for other iPod touch owners, if you're also having trouble opening the unit, my advice is to start opening from the top, right in between the power button and the Wifi antenna. From there, work your way down the length on either side with a precision flat head screwdriver and slowly shift. At least, that's the cruel, strong-arm method I used. If it's any consolation, replacement back panels and front bezels go for about 20 USD + shipping on eBay, so it's not all that costly to replace it. Then again, it's not all that costly to be careful while you're working. If I ever get this thing done, I wonder what kind of resale value it would even have. I guess I ought to evaluate its sound first. Anyway, I must entertain the guests now. Toodles.