Permalinks (don’t kill me) refuses to work..Yes, it results in a 404

From what you write it sounds like Apache isn’t reading/following the .htaccess at all. This can be the case if the AllowOverride setting is not active for that directory. (See this thread on StackOverflow for more information.)

<Directory /var/www/>
    Options  FollowSymLinks
    AllowOverride All
    Require all granted
</Directory>

Setting this (AllowOverride None -> AllowOverride All) and restarting Apache should solve the problem.