Is the led not lighting up? If so are you sure it’s the problem and not the switch? Did you try a different battery? From reading your posts it doesn’t seem as if you’ve really narrowed down the issue with the light. If it was me I would try a different battery and if that doesn’t make a difference then determine if the switch is the problem or not (easily done with scrap wire). Also did you check that the retaining rings are all nice and tight?

Edited to say that I forgot to mention that you can also remove the tube from the head and directly apply power to it to see if the led lights up or not.