I believe you installed Slackware and during the install, either selected a "safe" lilo installation, or told the installer to install lilo into the root partition instead of the MBR (master boot record).
Grub which you used before as the bootloader, is partly present in the MBR, but the rest of Grub was available in the /boot/grub directory of your Ubuntu partition, and you wiped that away.
What you can do is boot again from the Slackware install CD1 and when it pauses to let you select a kernel, pay close attention to what is on the screen. It will tell you that you can "boot your current installation in a pinch" or words like those, and tell you to enter
bare.i root=/dev/hda1 noinitrd ro
to boot directly into the Slackware that is installed on hard disk. Probably the partition your Slackware is installed is hda2, in that case the command line to enter would become
bare.i root=/dev/hda2 noinitrd ro
- you'll get the idea.
Once you've booted into your installed Slackware and logged in as root, open the file /etc/lilo.conf in an editor (vi or pine or whatever) and look for the line
(perhaps that 2 is another partition number in your case). You should install lilo into the MBR which you do by changing the above line to
Save the file, and install the bootloader by running the command
This will wipe the remnants of Grub from the master boot record.
Now, reboot again, without the CDROM in the drive, and Slackware's LILO boot prompt should appear.