Chosen Solution

Is the battery the reason it won’t charge or is it something else?

This is usually due to a bad battery. You can replace the battery if you want, but it requires soldering. I would suggest having it done professionally if you do not know how to solder if you really want to replace the battery. This iPod usually isn’t worth repairing these days since you can usually buy a good one for less then the cost of a battery replacement. If you still want to do it, here’s the guide. iPod Touch 3rd Generation Battery Replacement

Check your dock connector for debris, corrosion and bent pins, your cable as well and use an AC charger first. Once you have tried that , you should use the guides on the right side to get to your battery for a replacement.