This is a long shot, but could it be the USB chord which is bad? If you have another USB chord or can borrow one, try that. Another long shot is that it might be the USB on the phone itself. Another chord, especially if it works on another phone, will also tell you that.
Always good to try a different cord in this situation. If you can't figure it out (or even if you can), you may want to look into AirDroid for transferring between phone and comp.