Try this if all else fails.
Skip the LILO install and use the Slackware disk to rescue style boot.
Login as normal.
Download the latest Grub2 and it's dependencies from slackbuilds.org, install, and do this:
grub-mkconfig -o /boot/grub/grub.cfg
I did this using the default huge kernel and everything works.
Grub2 is a bit more of a pain to customize, but after you learn the ins and outs of creating the configuration files using a terminal, it's easy.