What happened to the old modem? If you've disposed of it then there's not much that you can do. The only person who could help you (IMO) would be the ISP; their logs ought to record your MAC. The guys there ought to be experts in networking and are best placed to help you. If they can't then I don't think you've got a chance.
But I'd be fascinated to know if anyone has a better answer.
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