explain in good english else no one cares to have a look
if u cant access any Linux on hdd,boot from a livecd,manually mount ur slackware partn.chroot into it.run "grub-install /dev/hdx" where hdx depends on ur hdd being sata or pata,find it with fdisk -l cmd.
I prefer GRUB to LILO and it seems GRUB got the future too.although suse uses lilo(u can install grub in suse too using yast).there is only one boot menu manager be there.
I'll explain in detail:
Warning:I hope u dont have made separate /boot partn in slackware else mount the /boot device(/dev/hdxx) to the mounted slack partns /boot directory.
boot a livecd(knoppix? etc) open a terminal as root and mount ur slack partn in it as rw.
now "chroot"(change root) into ur slackware partn(find it from ur linux partns or fdisk -l)
now if ur grub is available there,
if grub is completely lost,try setting grub manually.post here or refer "info grub" if grub-doc pkg is installed for this.
u can edit in slackware /boot/grub/menu.lst last a new line to add suse to it.for the syntax refer man grub and for suse kernel names etc refer suse lilo.conf