It sounds like the set-top box is using 'composite' video, where the video signal is carried by the yellow cable, while red and white carry the audio.
The TV likely has plugs for 'component' video, in which the video signal would be split up and carried over three cables, red, green and blue (in addition to separate audio cables).
If the TV doesn't have a dedicated plug for the yellow composite cable, it might have a setting to convert one of the component plugs into a composite plug. You should check your television's manual to see whether it says anything about that.