Do you have more than one CD-ROM? I can only boot off of one of my two CD-ROM drives. My system is set up like this:
hda hard drive w/ windows stuff
hdb hard drive w/ windows stuff
hdc dvd-rom drive
hdd cdrw drive
hde hard drive w/ linux (connected via PCI card that gives me two more IDE cable slots)
And for some reason, I can only with CD's from hdc, not hdd. If you have more than one CD-ROM drive, then try putting the disk in the other cdrom drive. Also, if you have a boot menu before LILO loads, (for me it's either F10 or F12, I forget which) you can tell it to only boot from the CD-ROM or Floppy for that one time, not having to mess around with the bios. Then if it can't boot from the CD-ROM, it'll let you try again, so put the CD into the other CD-ROM drive and try again. Unless you flashed your BIOS or something, I don't see why you shouldn't be able to boot from CD-ROM at all. Have you tried booting off of a slackware CD that you installed from?