I only briefly skimmed through the thread, but if you created a dedicated partition (or more) for Slackware in Windows XP, you likely need to change the partition type to linux, as I don't think Windows offers that ability. The easiest way to do this would be to find the partition you want to adjust (the command
lsblk might help with this), and then you'd want to change it using a program like fdisk. Run fdisk against your drive (if you only have one drive, it's like /dev/sda)
Then you'll want to hit p and enter to view the partitions on that drive and determine which partition(s) you need to adjust. Then press t and enter and it will ask you what partition. Press the number for the partition you want to change and it will ask what hex code to use. Press L and enter to verify that 20 is listed as "Linux filesystem". If it is, type 20 at the prompt and hit enter. Do this for any remaining partitions (note, if you have a swap partition, that will likely be 19 "Linux swap"). Once completed, hit w to write the changes to the disk and then q to exit.
Now you should be able to successfully start the installer and have it detect the drives.