Thanks for your help folks. The files is over 19Meg so I won't post it but I think I know what the problem is, I just don't know how to fix it.
At Jim's suggestion, I copy and pasted nine grouped scenes into a single timeline. They play alright right up to the last group and this is where the problematic text box is.
I have copied and pasted the last group into a new file. It works just fine and the text box is editable.
Throughout the animation, I have several full screen background images at 1920 x 1280. I have been making these backgrounds visible or invisible using opacity, they fade-in and then out again. Although they are invisible, they are, apparently, present for the entire length of the timeline, so one or more of these earlier large invisible images is physically on top of the problematic text box. That's why I can't select the text, even though I can move the entire box. If I bring the text box to the front, it is only at the front in that group. It is still behind an invisible background image in another group.
I don't know how to solve this. Any ideas?
I know, I should have done something simpler as a first project :?(