rescue e-mail

We have been trying to unlock and Apple ID password that we forgotten and then we finally got the right password but since it has been logged out so long we have to enter our security questions but we also forgot the answers to those. We tried changing the questions but once again since it has been logged out for so long we were not able to reset those either. We got it to send us an e-mail but the e-mail with the steps to change the questions was sent to an old e-mail account that has been deleted so we are not able to get in to the Apple ID account.