The process to do what was suggested in post 2 is pretty simple.
Boot into a distro that works
Mount the slackware partition
mount /dev/sda7 /mnt
Install grub on that partition
grub-install --root-directory=/mnt /dev/sda7
Add a chainloader entry to the grub.conf/menu.lst you boot from
You will need to make all these entries as root or use sudo