Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do what I can to provide the right answer to your question.
For the Menu on the TV to not appear, means the problem is not in the tuner, nor is it a problem with what signal source you could have on input, vs. what signal source you can select (and you cannot select the signal source, of course, when the TV's screen isn't showing anything!) The problem is obviously in the video circuitry - or doubtfully the screen (the backlight works, after all, at least)... or the connections to it, or among the video components and the screen, if the interior is the least bit dirty.
(So in plain words, a bit of re-seating, and cleaning, can't hurt and might help.)
I think that at this point, if no further progress with the case has been made, you need a service manual, so as to save a little money on swapping out components until you find out what defective component is responsible.
Service manuals for this model are available from this completely reliable vendor:
or from this vendor also, for a perhaps slightly smaller price by a dollar or so:
I hope that this information helps with the case. Let me know how it goes, I would care to hear more about this problem. Thanks.