You can delete the files extensions.* (extensions.rdf, extensions.cache, extensions.ini, extensions.sqlite) and compatibility.ini in the Firefox profile folder to reset the extensions registry. New files will be created when required.

See "Corrupt extension files": http://kb.mozillazine.org/Unable_to_install_themes_or_extensions

If you see disabled extensions that are not compatible on the next start in "Tools > Add-ons > Extensions" then click the "Find Updates" button to do a compatibility check.

Thankls. I've tried that, twice in fact, and I am still having the problem.

Does it also work if you click "Check for Updates" instead of reinstalling?

It would suggest that there is a problem with the file extensions.rdf, so make sure that you do not have security or cleanup software messing with files in the Firefox Profile Folder.

A workaround for this is to manually install the dictionary files. Download the .xpi file from https://addons.mozilla.org/en-US/firefox/addon/3366/ (right-click on the "Add to Firefox" button and choose "Save Link As").

This should save a file called british_english_dictionary_1.19-fx+zm+tb.xpi, this file is a zip file. Edit that file with a zip utility, if you do not already have one, one I recommend is 7-Zip available from http://www.7-zip.org/

Inside that file you will find a directory called dictionaries containing 3 files. Extract en-GB.aff and en-GB.dic

Copy those 2 files to the dictionaries folder inside the Firefox installation directory, default location C:\Program Files\Mozilla Firefox\dictionaries

This will add the en-GB dictionary and you will no longer need the extension.