Probably no need to buy anything new.
caveat - this discussion assumes that you are using a broadband router and more than one computer. If you have multiple computers hooked up directly to the broadband modem through a hub/switch without using a router, then you will have problems unless your isp specifically allows you to get more than one ip address from your isp. A broadband router requires only a single address from your isp and is usually cheaper.
To set up your LAN's ip addresses, you usually have 2 options. First, you let your router assign ip addresses via DHCP. When a computer is turned on, the network drivers broadcast a request for a DHCP server to tell it what ip address it should be. If there is a dhcp server around, it responds back with some config information, usually an ip address for the client computer, the ip address of the gateway, and the ip address of the DNS server. In the case of a home lan, the reply will usually be something like this:
ip address - 192.168.0.xxx (xxx is usually between 2 and 254)
gateway - 192.168.0.1
DNS - 192.168.0.1
This is because home broadband routers are often (usually?) set up as 192.168.0.1.
The second way to set up your lan is to manually assign ip addresses. There are security and usability benefits to this especially if you're using wireless, but it requires some network administration because you have to manually go to the tcp-ip properties for every computer and manually enter in that computer's ip address, the address of it's gateway, and the address of the dns server.
Problems arise when you change how you do things. For example, if you start off using manual ip addresses and have 2 computers plus your router, you could have something like this:
192.168.0.1 - router
192.168.0.2 - computer 1
192.168.0.3 - computer 2
But what if you enable DHCP on your router and add a third computer? Sometimes you could get this:
192.168.0.1 - router
192.168.0.2 - computer 1
192.168.0.3 - computer 2
192.168.0.3 - computer 3 (dhcp assigned address)
But what if computer 1 isn't turned on when computer 3 makes it's DHCP query? Then you could get this:
192.168.0.1 - router
192.168.0.2 - computer 3 (dhcp assigned)
192.168.0.3 - computer 2
Then if you turn computer 1 back on, you'd have:
192.168.0.1 - router
192.168.0.2 - computer 3 (dhcp assigned)
192.168.0.2 - computer 1
192.168.0.3 - computer 2
This is an obvious conflict, and neither computer 1 or 3 will work reliably on the network until it's cleared up.
So.... what do you do?
Either manually set each computer to it's own unique ip address that is compatible with the router, (usually 192.168.0.x but it could be 192.168.1.x, etc) or go into the router configuration and enable DHCP, and then set each computer to automatically get it's ip address via dhcp.
There are other ways to solve this, such as setting the dhcp server to assign addresses in a specific range (say 100-110) but again that requires some level of network management to keep it all straight. I personally set manual ip addresses for my wired computers and have my and my wife's laptops configure wirelessly through dhcp. Not quite as secure as manual configurations, but it keeps the configuration changes to a minimum when we travel.
