Make sure that the component cable is set to whatever input you have the cables plugged into. For example, if you are using the component connection, RED-GREEN-BLUE and then WHITE-RED for your audio, make sure the switch is set to HDTV. If you are using standard connection, YELLOW-WHITE-RED, then make sure it is set to TV.
If this still doesn't work, try a different pair of video cables and if the same results are coming up, you will need to have the board repaired. You can not just replace the motherboard either or you will not be able to play games on the system, make sure to have the actual board repaired.
Yes there are ways to repair the board out there but board repairs are different from replacing it. If you don't use the right equipment, you pose a greater risk of damaging the board more than it is already. It's best to have the system repaired by a professional that provides a warranty on their work.