A live CD will boot the system long before LILO kicks in, so I would doubt that's the problem. You should check your BIOS to make sure booting from CD is enabled and ahead of booting from the hard drive. It could be that the Helix Live CD lacks certain drivers for your desktop, or that certain modules must be loaded before it can boot successfully. You may have to pass options to the kernel to get it to work. You should provide the entire error if possible, and tell us at which stage the error occurs.
I don't know anything about the Helix Live CD, so I can't help you beyond that. You may wish to try passing 'noapic', 'acpi=off', 'nolapic', etc. to the kernel to see if that helps.