First question is do you know what NAT stands for? It is Network Address Translation. In simple terms, it assigns IP address to your network. Unless you've fooled around the settings should be unchanged.
For the simplest possible solution, try shutting down ALL the equipment. Then boot in this order: the cable/DSL modem, the router, the switch, the Xbox console. Give the modem and router plenty of time (30-40 seconds) before booting the next device.
Come back if this doesn't work.