Have you configured the IP addresses in the TCP/IP Properties of the two network adapters?
If not, in XP open the Network Connections folder ("Control Panel > Network Connections"), right click the Local Area Connection and select Properties. Highlight the entry for "Internet Protocol (TCP/IP)" and click the Properties button.
Click "Use the following IP address" and type in:
IP address 192.168.3.1
Subnet Mask 255.255.255.0
Leave the Default Gateway and DNS Server addresses blank because this isn't an Internet connection. I selected that IP address to avoid conflict with your router's address which could have 0, 1 or 2 as the third 'octet' (number) of its address. I'm not familiar with the interface of an Xbox, but give it the address 192.168.3.2 with the *same* Subnet Mask of 255.255.255.0
If you're using third-party firewall software in the PC, it may need to be configured to allow access to the 192.168.3.1 and 192.168.3.2 IP addresses.
If the Local Area Connection is normally used to connect to your router for internet access, you will need to go back into the TCP/IP Properties and set *BOTH* IP and DNS sections back to getting their addresses automatically.