Facing TV Problems? Ask a TV Technician.
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The remote may be defective. (Can another remote work with this TV? Would you like to try replacing the remote?)
The TV's receiver (a little module that senses the pulses of light (usually infrared and invisible light) the remote is sending to it) may be defective. That does happen, too.
The TV's logic board may be having problems, too, by the sound of it. When you press the MENU button on the TV, after it has locked up and refused to respond to the remote, do you get no response then, no Menu on the TV's screen? if that's what happens, the TV is defective and will require a more-than-trifling repair: The infrared sensor module is a relatively small and cheap part, but the logic board or other parts would cost something considerable.
Let me know which of these cases seems most likely, and what you would like to do.