IP Conflict

On Win XP machines, whether I use a wireless router, or a wired hub, I receive an icon that appears in my tray informing me that there is an IP Conflict.
Connecting just two machines at a time, neither will connect to the internet when this takes place.
If I unplug one or the other from either the router, hub or LAN card, the other connects immediately.
I am connecting from an always on, analog, DSL modem, configured from the first machine.
Have had great difficulties establishing a network, even using the XP network wizard.
My question is: Dismissing the idea of the network, how can I resolve the IP Conflict issue so that these machines can at least share an internet connection.