Is this something I could fix

David, when you say the "prongs are broken" and you are referring to the dock connector, this most certainly will stop your iPod from charging. The connector can be replaced. Here is the big but I'd like to say that this is not an easy job and does require some very good soldering skills as well as great tools. Hot-air station would be the best, but it can be done with a good soldering iron, a steady hands and some good magnifying light. In order to remove it, disassemble the iPod completely by using one of these guides.. Then you will have to de-solder the solder from the two anchors of the dock connector. Best way to do that is by using braid or a solder sucker. After that you will have to de-solder each and everyone of the pins (30 of those) again, a solder sucker or braid will definitely be a must. Once you have it all de-soldered, clean it and replace the dock connector by soldering all the contacts and anchors. Make sure that you are very careful not to bridge the contacts with solder. Check this video for what needs to be done and if you are up to the challenge. It is a 2nd gen iPod but the same idea. the part is available at places like this. If you are not sure if you want to do that job, there are commercial places available that will fix it for you for around $60-$80. Hope this helps, good luck.