Vekia,
Thanks for coming back on this, which I've now figured out.
I'm running PrestaShop in a subdirectory, using the instructions at http://dobetterit.com/prestashop-in-sub-folder/
What happened was instead of accessing the BO as http://mydomain/admin12345 I ended up accessing as http://mydomain/subdir/admin12345.
When the subdirectory was included, all the BO pages looked fine, but I noticed that I couldn't see the category tree and after digging deeper found that JQuery and several other .js files were not being loaded. I saw the errors
"ReferenceError: $ is not defined" and so went to look at why this might be.
Anyway, after taking the subdirectory out of the path, I found that everything was actually working correctly.
I hope this helps anyone using this sort of config, should they run into the problem I had.
Thanks again for coming back to me on this.
Alan