Why does my back button not work?

This is usually a clickwheel issue. The clickwheel is sort of independently replaceable, so you may not need a new case, but it is not as easy. It is easier to find complete cases then it is to find a bare clickwheel since it is so hard to change the clickwheel in the Nano.

The downside is your serial number won’t match, but you will also find the repair to be a lot easier. If you want to preserve that, you will need to pull it out from the new case and swap it over.

Follow this guide to get the iPod apart and see if you handle a bare clickwheel swap, or you need to change the case.