From what I've read, some of which was explained by a former AppleCare Helpcenter employee. When trying to resolve the customer code error you must explain that you have a problem with your Apple ID and proceed from there. The former employee explained that them asking for your serial# is a way of tracking the issue/call. If you present it as an Apple ID problem, they in turn ask you for that and use that to track the issue/call. Maybe this isn't the case with everyone and maybe this has changed, but it is worth a try.