In that case the tuner - the part in which the cable plugs in and in where the tv channel is selected, the data extracted and separated in video and audio - is defective and it will have to be replaced.
The part is quite cheap - $25 - but its removal and replacement is a complicated job (lots of very fine solderings required) that it would be best if you would leave it to someone with experience. You will probably have to take the tv to a repair shop, it will all cost you around $150.