You will need to boot with your installation media.
After logging in as root, don't run setup again but issue following command:
take a note of the output and report it here.
You can also tell how these partitions are used.
Consider the partitions that have Linux as System (as shown in fdisk -l) and do this (I assume /dev/sda1 has System Linux, adapt accordingly for the other ones case occuring):
mount -t auto /dev/sda1 /P1
ls -1 /P1
So you will know what's in it. I assume you have a / (root) partition for Slackware, maybe another one for /home.
If you report the layout you find we will be able to help you.
Also if you find the root partition, let's say as /P1 (with /etc in it), please do
and tell us what you find.
To avoid you the hassle of copying all that on a paper you could also mount an USB key. Plug it in, assuming it is recognized as /dev/sdb1 (you can check with cat /proc/partitions), mount it:
mount -t auto /dev/sdb1 /key
After that you can copy the file to the key, e.g.
cp /P1/etc/fstab /key/fstab.txt
The same way you can copy the results of a command, e.g.
fdisk -l > /key/fdisk.txt
ls -l /P1 > /key/lsP1.txt
When copying files is over, don't forget to umount the key:
EDIT Again, It seems that I like to complicate things uselessly - just boot your system using the DVD as told in the first screen of the installer to get the info we need