The problem is that when the lilo part of the installation failed, it did not install the lilo boot loader on the master boot record (MBR). When you restarted with the CDROM, all it did was boot from the CDROM, not the install you just completed. As I see it, you have 2 main options:
1. Boot from the CDROM, mount your hard drive, edit the /etc/lilo.conf file to the correct specs (you would have to tell us your hard drive setup in order for us to tell you the proper config), run "/sbin/lilo" to install lilo, and reboot without the CDROM.
2. Reinstall Slack, but use manual configuration for lilo. Again, we would need to know your hard drive setup to tell you the appropriate settings.
Beyond those 2, I would suggest 2 more things:
1. If this is your first try at Linux, I would try something like Mandrake, Fedora, SuSE, etc. Mandrake is my favorite for new *nix'ers.
2. If you insist on Slackware, which is not known as a newbie friendly distro, I'd try a newer version. I'm running Slack 10 on my laptop. It is compiled for i486, so even the newest version will run well on older hardware.