As you have seen, you can't have two of the same IPs on the same network, but you also can't have the same computer on the same subnet running with two IPs.
While the first part of this sentence is correct - you shouldn't have two of the same IPs on a network - the second part is not. If the computer has two (or more) network cards it can have two IP addresses. The IP address is for the card. The server in our office has two wired cards, and each have unique IP addresses. All modern laptops have a LAN port and a wireless card, and both can be used at the same time, as long as each has a unique IP address.
