Unfortunately, many extensions were not updated in time for a change in Firefox 40, which is that the "widget" module was removed. This was the old method for adding a button to the toolbar, and extensions which weren't updated to the new method by now seem to stop working.

Since this particular extension was released under the Mozilla Public License version 2.0, I can post a modified version which works around the issue by stripping out the code related to the toolbar button: Instead of my modified version, see: https://support.mozilla.org/questions/1078319#answer-771886

After downloading that file, drag and drop it onto a page in an open Firefox tab to start the install process. This is not an official signed version, so it will be blocked in Firefox 41, but perhaps it will bridge the gap until the author or someone else posts an official new version.

Now... should you trust this unofficial version? That's up to you. If you want to do the edit manually, here are the steps:

(1) Right-click the "Add to Firefox" button on the add-on's page and use "Save Link As" to save the .xpi file to a convenient location, such as your Downloads folder.

https://addons.mozilla.org/firefox/addon/translator/ => C:\Users\username\Downloads\

(2) Using 7-zip (http://www.7-zip.org/) or your favorite ZIP software, unzip the extension file to a new "Translator" folder in the same location.

=> C:\Users\username\Downloads\Translator

(3) Click into the Translator folder and drill down to main.js and open it in a text editor (not a word processor that might try to format things)

C:\Users\username\Downloads\Translator\resources\translator\lib

If you need a text editor, you could try Notepad++ from http://notepad-plus-plus.org/

(4) Edit lines 1-2 as follows:

From:

var widgets = require('widget')
    , pageMod = require('page-mod')

To:

var pageMod = require('page-mod')

(5) Comment out (deactivate) lines 155-172 by adding /* on line 154 and */ on line 173.

Note: those line numbers are after you make the edit in Step 4.

(6) Save the changes to main.js, then zip up the contents of the "Translator" folder (not including the folder itself) into a "Translator.xpi" file. Note: .xpi, not .zip.

In the file I posted, I also added (HACKED=>no widget) into the install.rdf file so that would show up when you click the "More" link for the extension on the Add-ons page, but for your own use, that's probably not necessary.

(7) Drag and drop the Translator.xpi file into the page area of an open Firefox tab. Firefox should ask you whether you want to install an unverified extension, which you can go ahead and allow.

(8) In a regular page, select text and right-click, and the item should be back on the menu.

The author has posted a new version on the Add-ons site for review. Once it is approved it will be signed and added to the main page, but if you like having the toolbar button to send the current page to Google Translate, you could install it now from the "versions" page:

https://addons.mozilla.org/firefox/addon/translator/versions/

The updated version is live on the main page: https://addons.mozilla.org/firefox/addon/translator/

If you want a laugh, use the text-to-speech feature to read you the lyrics of a love song.