This may be too late, you are probably not at the library, but it might help next time.
Any time you are using a mobile computer in a public wireless environment you should have your networking environment configured to use DHCP and receive your IP address from the router. There are lots of reasons for the assignment of static IP addresses, but most of those are in what I will call a fixed network environment. Even in a wireless environment, it might be advantagious to ensure that a particular computer receives a known IP address, but this should be done by establishing a 'reservation' at the router so that the mobil computer is free to wander and will be assigned the desired address when associated with that particular router.
If your computer was setup to get the IP address via DHCP, then someone else's computer was in the wrong having hard assigned an IP address to their network interface. If your computer is not configured to use DHCP, then you should change it. If your computer is configured to use DHCP, then you need to force it to drop the address and have another one allocated.
I run UNIX on all of my PCs, so Im not in a position to describe how to do this under windows. I'd guess it can be done with the 'ipconfig' command mentioned in another answer to your question.
As for the meaning of the message that you got; it goes like this: The IP address that you assigned to your wireless interface was the same as one dynamically assigned to another computer; both were associated with the same wireless portal (router). The probelm caused when two computers have the same IP address is that the router can (should) associate one real hardware (MAC) address with an IP address; if the router has associated only one computer to the IP address, then messages that the router receives for that address may be sent to the wrong computer. It can be more complicated than this, and there might not be any noticable symptoms, but if you see this message then either you
After understanding the message that popped up, it should be clear why you would want to force a new IP address to be assigned to your computer if you were already using DHCP to obtain the IP address -- the other user is either unaware that they are stompping on the address, or are doing it on purpose; in either case it can cause you problems.
You mentioned 'your dialup guy.' Assuming that you are dialing in from home to access the internet, then I have to ask: does your dial-up ISP assign you a static address? If so, you will need to reconfigure your network environment to use DHCP whenever you the wireless interface.