First question - is there a particular reason for connecting the X-box to the PC rather than directly to the router?
If it has to connect to the PC, you need to enable "Internet Connection Sharing" on the actual internet connection in the PC (the connection to the modem). This will automatically configure the Local Area Connection with the fixed IP address 192.168.0.1 and subnet mask 255.255.255.0 Additionally, it enables the PC as a DHCP server to allocate the addresses (IP, Subnet Mask, Default Gateway and DNS Server) to the "client", in this case the X-box. The network adapter in the X-box should therefore be set to get its IP address automatically.
To enable “Internet Connection Sharing” in Windows XP, open the Network Connections folder, right click the actual internet connection (modem connection), select Properties and then the Advanced tab. Tick the box “Allow other network users...etc”.
If you run the Zone Alarm firewall in your “host” PC, the Internet Zone Security level must be reduced from High to Medium or “ICS” traffic will be blocked. Whatever firewall software you run in the PC, it will need to allow access to the X-box in its "trusted" area.
Becasuse Internet Connection Sharing operates in the 192.168.0.xxx range, your router will have to operate and allocate IP addresses in a different range (i.e. with the third octet of the IP addresses a value other than "0", which may already be the case).