IPod Touch charges then disconnects?

I have a 32GB 4th Generation iPod Touch and recently when I connect it to my (5-year-old) computer via the Apple USB cord, it connects for a split second then disconnects. If my iPod was dead prior to plugging it in, it stays connected long enough to turn back on, but once it turns on, it disconnects. I don't think that the wire is the problem because when I connect it to my XBOX, it works fine. And the iPod is not the issue because it charges with the XBOX and my iHome without issues. Also, I'm not convinced that it is a problem with the USB port because this happens in all three of my available USB slots, two of which are rarely used. Any ideas?