My battery died, can be replaced?

Yes, the battery on on iPod Touch can be replaced. You can find a good quality replacement here. It will require that the connections be soldered however so if you are uncomfortable with that, it is best to have it done by a repair shop.

iFixit does not have a specific guide for battery replacement but you can follow this one to open the device and access the battery. I would highly recommend that you go through the entire guide first to see what level of effort is required before you start.