Trivia Cracker requires you be signed into Google Chrome with a Google account, in order to check the status of your free trial or purchase license.
You can sign in to Google Chrome by going to chrome://chrome-signin/?source=0 and signing in. If successful, you should see your name in the top right of the Google Chrome browser:
If you see a yellow caution icon next to your name, something went wrong, and you will need to sign in again.
After signing in successfully, reload Trivia Crack on Facebook and the button should now work.