File browser not showing when trying to Add New

I don’t get the Browser tab at right column when trying to Add New file (package), just the Upload option.

It’s strange because I’ve put the same settings at other site, and there it does show up.

I’ve tried to put Server File Browser Base Dir setting to many different directories:
– At hosting’s home directory.
– At WordPress base dir.
– At an inner dir below WP base dir.
– Inside /wp-content/

…And no way – there’s no Browser tab when I try to Add New download.

Might it be a matter of permissions or something like that?

Thanks in advance.

PS: Browser access in this blog, they are set, by default, to Contributor and Administrator. I’ve just removed Contributor and left Administrator alone in those settings, but there’s no change at all. When I click on Add New, only Upload tab shows up 🙁