Instructions
Make sure your TV monitor is turned on, since sound will still play on the system without the TV on.
Check the RCA connection cables (colored red, white and yellow) on the back of the TV to ensure the colors are matched. Switch the wires if yellow is accidentally plugged into white and so on.
Push the TV/Video button on the front of your TV to change input channels. The Xbox picture should show up on one of the auxiliary channels, like "Video 1" or "Video 2" or "Game."
Unplug the console if you are still experiencing problems. Allow the console to sit for a minute, reconnect the RCA cables into their appropriate plugs, reconnect the main power source and reconnect controllers if needed. Test your system.
Take your console back to the store you bought it from for an exchange if you are still experiencing problems, since the problem is most likely a wiring problem within the console itself. Contact the Xbox company directly if your warranty is no longer valid (see Resources).