Have you tried turning everything off, then restarting the network?
Start the modem first, then the router, then your devices PC/xbox or whatever. You shouldn't have any issues with DHCP or xbox live with a nat'd router. If you are hosting games, you will need to setup the xbox on the DMZ or use portforwarding, no need for static IP's unless you are running a marathon gaming session, dynamic IP's usually last for several days. The DMZ and Port forwarding are a bit risky for the rest of the network