You have to have a boot loader on your system at some point. The best
place to put it is on the MBR of your first hard drive. LILO is a good
boot loader, you should install it.
The reason your CD boots the system is that it essentially has a boot
loader on the first few bytes.
You have two options, I like the first better:
1) I think when you boot with the CD (haven't done this in a while),
you will get a boot prompt. Here you want to say:
mount root=/dev/hda1 (where /dev/hda1 is your root partition)
Once your computer boots up (into your fresh install), log in as root,
and run liloconfig. Follow the steps.
2) You can boot with the CD, mount your root directory, to /mnt, run
liloconfig and follow the steps to install LILO. This isn't necessarily
as easy as it sounds because you might have to trick liloconfig to
install LILO in the right place.