The only uniquely identifiable information you can use is the IP address. MACs cannot be used to identify because dialup users would be able to change them as easily as they can change IPs, as the MAC they receive is the device they're connected to, not their own device. There are similar problems for other connections. The lookups to find these addresses are generally not routable, so they won't go across the internet. Even if all of these problems were surmounted, it's trivially easy to change the MAC address of your device.
NAT boxes do not have a particular signature that they place on packets -- they only work by keeping track of connections and translating/retransmitting the packet with the source addresses fixed to the NAT box address, and vice versa. Everything they do is transparent to the external connection.
Your best bet is to find some sort of IP-based solution.
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