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If you need another ethernet cable, you can find one easily online or at any electronics store. Your modem is the device that brings an internet connection into your home. Many routers do not broadcast as fast as the modem they're hooked up to, which can hamper connection speeds. You may have enough space to plug both your Xbox and router into the modem.  Wait at least one minute. You could take a small break, just to be safe.  The devices should be connected without any additional configuration.
Unplug any cable connecting your router to your Xbox. Unplug the cable connecting the modem to the router, if you need to. Plug the Xbox directly to the modem. Unplug your modem from the power source. Plug the modem back in and wait for all the lights to return to their normal state. Turn the Xbox back on.