How to Connect Computer and Xbox 360 to Internet Simultaneously
You cannot share a single wired Ethernet port between two devices. Ethernet is point-to-point; the Xbox 360 needs its own dedicated path to the router.
The Right Way: Use a Router
Modem → Router WAN port (Ethernet).
Router LAN ports → PC and Xbox 360 (two Ethernet cables).
Configure router (DHCP on, UPnP enabled for open NAT).
Wireless Alternative
Same modem → router setup.
Connect PC via Ethernet (preferred) or Wi-Fi.
Connect Xbox 360 via Wi-Fi (built-in on S/E models; USB adapter for original “fat” 360).