Then you have a defective TV- there's no way around that.
Red,White and Yellow connect to the Red,White and Green jacks respectively- then you select "Video" from the Input selections- and you're saying you have no "Video" option.
Red,Blue,Green,Red and White connect to those same colored jacks, and then you select "Component" to get a full color picture- and you're saying you get a black and white picture on this Input.
These symptoms indicate that your TV is defective and should be returned to the retailer for an exchange.
However you can try a hard reboot of the set to see if that helps.
Disconnect the set from power then press and hold the power button on the TV itself (not the remote) for 10 seconds and release. Wait a minute then plug it back in and press power once. Select component using the RGB cables and see if the picture is still in black and white.
If so, then do you have another source such as a DVD player that you can attempt to connect to the TV to see if the same issue occurs?