It is completely fixable i have done it to a friends ipod touch 2g (mc), just like your one.
1st. buy this battery: http://cgi.ebay.com.au/Original-New-Battery-iPod-Touch-2G-2nd-Gen-Tools-/270729364924?pt=AU_MobilePhoneAccessories&hash=item3f08ba45bc
2nd. Follow this guide...
btw i feel this a good time to remind you guys that sea of thieves was made by rare, who also made DKC1-3 and DK64, alongside banjo kazooie and conker's bad fur day