As you suggest, it should be possible to view your gallery's XML data by going directly to the following URL in a browser:
However, going directly to this URL results in an error 403 (access denied) message.
Whatever is preventing direct access to this PHP file is the cause of your problem.
However, there are several possible causes...
(1) Check that the permissions on the 'config.php' file (inside the 'wp-juicebox' folder) are not too restrictive.
Also, check the permissions on the 'wp-juicebox' folder itself.
You should be able to check and change permissions using an FTP program such as Filezilla or via your hosting account's online control panel.
Default permissions of 755 for folders and 644 for files should be fine.
(2) Check to see if you have any .htaccess files on your web server (most likely in your root directory) which contain rules which block direct access to PHP files.
If you find any entries in any .htaccess file such as the following, then try removing them to see if this resolves your problem.
(3) Check to see if you have any plugin's installed which might somehow be interfering with WP-Juicebox's functionality.
Deactivate all your plugins (other than WP-Juicebox) and reactivate them one by one (checking your gallery after each one) to see if you can find a conflicting plugin.
(4) Check in with your web host to see if they have recently introduced any security measures which might be blocking direct access to the 'config.php' file.
Since a few days, I have the " config file not found" without having done any modifications...
If things were working fine but now they are not (without you having done anything yourself), then this suggests that something may have changed on your web server so I'd certainly ask your web host if they have made any changes recently to your hosting account which might account for your problem. They should hopefully be able to shed some light on the issue.
With the new Box interface of WP, I even couldn't create any new gallery with Juicebox, the button had disapered.
With regard to not seeing an 'Add Juicebox Gallery' button, please see this forum post which might help.