|Is that device a SOHO router? If it is, then something is wrong with the configuration. Open a command prompt window on both PC's and type the following command:|
and paste the output of both PC's in here so we can look at it.
If the device is just a basic switch, then you would need something to do NAT for you.
NAT = Network Address Translation
NAT allows many computers (IP addresses) to access the internet through a single IP address. Windows XP has ICS (internet connection sharing) built into it and you could use that to share the internet. This would however require two network interfaces in one of your computers that would then run ICS and share with the other computer.
The simpler solution is to buy a SOHO router with 4 LAN ports and use that. It will have everything you need like NAT and also a firewall (for your protection) that would allow multiple computers to connect to the internet through your single internet connection (IP address as provided by your ISP).