The pictures are of an Axxera tv. Make sure it says Air and not Cable. I did that once until I realized that the tv was doing exactly what I was incorrectly asking it to do.
That pretty little light just means signal booster has power and is on. If the cables are loose, missing or disconnected that light won't throw you a hint that something is wrong. Go there and then hunt for the splitter('s). I figure you already checked the TV end.