disk space utilization - df shows bad information on partition usage

I've tried to deal with this for days now with no luck. In this forum and also in other ones I can see a lot of discussion about this but none of the solutions have worked for me.

My current situation is that I've got some GBs "missing" that I can't free or find anywhere. I guess this is some kind of problem like memory leaks that only get fixed when rebooting, but I just would like to ask if someone has a better idea because there are currently a few customers on that server.

Here are some of the commands I've seen in other threads and my particular outputs:

Filesystem            Size  Used Avail Use% Mounted on
/dev/sda1              19G   16G  1.8G  90% /

tmpfs                 384M     0  384M   0% /lib/init/rw
udev                   10M  1.2M  8.9M  12% /dev
tmpfs                 384M     0  384M   0% /dev/shm

4.8M    /bin
27M /boot
0   /cdrom

1.2M    /dev
8.8M    /emul
504M    /etc
4.0K    /grubconf
88K /home
60K /images
0   /initrd.img
147M    /lib
0   /lib32
0   /lib64

16K /lost+found
12K /media
4.0K    /mnt
4.4M    /opt
777M    /proc
57M /root
4.7M    /sbin
4.0K    /selinux
4.0K    /srv
0   /sys

4.0K    /tmp
332M    /usr
471M    /var
0   /vmlinuz

(no output)

(no output)

-r-------- 1 root    root 777M 2015-07-21 06:19 /proc/kcore
-rw------- 1 root    root  64M 2015-07-09 03:31 /sys/devices/pci0000:00/0000:00:06.0/0000:01:04.0/resource0

-rw-r----- 1 root    adm   49M 2015-07-21 06:19 /var/log/auth.log
-rw-r----- 1 root    adm  174M 2015-07-19 06:25 /var/log/auth.log.1
-rw-rw---- 1 control mail 100M 2015-07-21 06:00 /var/mail/control

If you make the maths from du, for example, you get a few GBs, but nothing close to 16GB.

/ is ext3.

OS is Debian 6.0

is there anything am I missing here?