I didn't spend more time to find the cause and the fix of this issue back then, but today I had to work on a site with the same issue: No Languages Available on the Languages Manager and a requirement by the site owner to fix this.
So after going round around, I discovered that for this new particularly website the issue was in the database.
In order for the Language Installer to find Languages packs, there must be the following records in the database:
Table: #__extensions
A package type extension with name: English (en-GB) Language Pack
Table: #__update_sites
A record for this site: Name: Accredited Joomla! Translations
, Type: collection
, Location: https://update.joomla.org/language/translationlist_3.xml
Table: #__update_sites_extensions
A record that will join the extension from first table with the update site from the second table. So this record should have the id of the English (en-GB) Language Pack
extension, and the id of Accredited Joomla! Translations
update site.
In my case it was the English (en-GB) Language Pack
package extension missing from the extensions tables at first place. Not sure how this happened initially, since this package is also a protected extension, but that was the fact.
So I had to add the extension in the database:
INSERT INTO `#__extensions` (`name`, `type`, `element`, `folder`, `client_id`, `enabled`, `access`, `protected`, `manifest_cache`, `params`, `custom_data`, `system_data`, `checked_out`, `checked_out_time`, `ordering`, `state`)
VALUES
('English (en-GB) Language Pack', 'package', 'pkg_en-GB', '', 0, 1, 1, 1, '{\"name\":\"English (en-GB) Language Pack\",\"type\":\"package\",\"creationDate\":\"December 2016\",\"author\":\"Joomla! Project\",\"copyright\":\"Copyright (C) 2005 - 2016 Open Source Matters, Inc. All rights reserved.\",\"authorEmail\":\"admin@joomla.org\",\"authorUrl\":\"www.joomla.org\",\"version\":\"3.6.5.1\",\"description\":\"en-GB language pack\",\"group\":\"\",\"filename\":\"pkg_en-GB\"}', '', '', '', 0, '0000-00-00 00:00:00', 0, 0);
After adding the extension, I found out that the only other thing I had to, was to go into the Extensions: Update Sites and Rebuild the Update Sites. This is taking care of the rest, that is adding the Update Site and join the 2 records.
After that Languages became available for installation in the Language Installer in the backend.