The problem was that mail() method worked when invoked with php -r "mail('address@domain.tld', 'Subject', 'Message'); but when I tried it via the web server (apache in my case), in a php script, no email was sent and the mail method returned false. On top of this no error was displayed or logged anywhere not even error_get_last function did not return anything and I had display_errors and error_reporting activated and full E_ALL.
After trying all the possible tests that I could imagine I tried to send an email by executing the sendmail command form a php script. When I tried php’s shell_exec with sendmail:
shell_exec('/usr/sbin/sendmail');
and checked apache’s error logs got the error sh: /usr/sbin/sendmail: Permission denied. After I got this error it was obvious that the fix was to change the permissions for /var/qmail/bin/qmail-inject and /var/qmail/bin/sendmail so that apache can execute them.
Then said to myself: Happy developing! and that was it.