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...
@K3Nv2 I got some cheapies at wallys, that are pretty good, already have lost a few expensive ones (one falls out and gone, can't find) while cutting grass so bought some cheap ones, and of course never lose these cheap ones. (Cheap meaning only $35, compared to air buds which I only have 1 of 2 now)