We will answer this one straight, because the symptom tells you more than you might think, and knowing what it means keeps you from spending money in the wrong place.
Sound and picture are separate paths inside the set. Audio working tells you the power supply is at least partly delivering and the main board is alive. The failure lives in the picture path, and on modern LED-backlit sets the most common picture-path failure is the backlight: the LED strips behind the panel, or the driver circuit feeding them.
There is a test you can do in thirty seconds with a flashlight. Turn the TV on, dim the room, and shine a bright flashlight at the screen at a slight angle. Look for a faint image hiding in the glare.
- If you can see a picture in the flashlight, the panel is producing an image and the backlight (or its driver) is what died. That is the classic backlight failure shape, and it is a real repair rather than a mystery.
- If there is nothing at all under the flashlight, the failure is deeper in the picture path (main board or panel), and that is diagnosis territory rather than a known-part answer.
One honest note on the economics: flat-panel repair is parts-and-labor sensitive, and on some sets the answer is "not worth it." Get a real diagnosis before spending on parts, and be suspicious of anyone who quotes a repair without opening the set. If it is not worth fixing, you deserve to hear that in plain words.
Take this as diagnosis information rather than a service pitch. If you run the flashlight test, post what you saw; the community here can tell you what branch of the tree your set is on.