Why doesn't my iPod sync with iTunes via USB 2.0?

My iPod mini has recently suffered from battery issues, but it still charges. By battery issues, it has bad battery life. If it has a full charge, the battery will typically lower to 25% within a minute. I will replace the battery soon, but I don't think that is the cause of my problem. When I plug my iPod into my computer, it doesn't show up, and doesn't sync. The source of the problem is not my computer, as I have tried to sync the iPod with a PC running Windows 8.1 64bit, an iMac running Mavericks, and a MacBook Air running El Capitan. The iTunes versions are up to date on all operating systems. On some occasions, iTunes has given me an error message which told me to restore my iPod. When I selected the option, the iPod then ejected itself before anything could happen. I suspect the problem could be with the logic board. I am fairly new to these components, so any advice is helpful.