LiLo is the boot loader. it's what loads linux and allows your machine to boot. if it didn't get installed correctly you wouldn't be able to boot your computer
*edit=I just noticed that that you have a working boot disk*
You should be able to run "pkgtool" in the terminal (konsole I'm guessing) then select "setup" and then "liloconfig" (with the spacebar to select it) and re run the part of the script that installs Lilo. I usually put lilo on the MBR on the first Hard Disk... the third option listed as "possibly unsafe"
Post any errors from that.
*/edit*
Slackware Disk 1 is sort of a "LiveCD" but probably not terribly usefull for someone not comfortable with the CLI, but it may be enough to get you into your system to find the problems.
Stick in CD-1 and re-boot the computer, at the
first prompt (where you probably typed something like "huge26.s" or just pressed "enter" there is a bunch of stuff on the screen that stuff will change if you type "alt-F2"(or F3,F4... i forget how many screens there are) anyways, on one of those screens there should be something that tells you how too boot if you are having problems with a new kernel something like 'linux root=/dev/hda1 ro ....' I really don't remember but it's something along those lines.
type that in and it should boot your Slackware install using the kernel from the disk (Not terribly important at the moment, we just want in to access the file /etc/lilo.conf)
Once you get in to the Slackware install you'll be at the CLI again, typing "xwmconfig" will let you pick your GUI xfce or kde should be fine. then "startx" should give you a basic GUI environment (Low resolution likely not what you'll want when you get the booting problem fixed, but again, we just need to look at and fix some files.
If you have wired Internet (wifi probably won't work without more tweaking) you should have internet access from your slackware. then you can just find the file in whatever file browser you have open it up and copy/paste it here... following trashbird1240s directions... lots of information can be
very helpful.
Don't edit any files, because my directions will have you in there as the root user and as root you could easily break your system (more than it may already be).
If the directions above don't work. go download a new LiveCD (Knoppix, DamnSmallLinux, or other ones mentioned in this thread.) and boot it. it should work fine as a full system running from CD and RAM... no need for a hard drive. From the live cd you should be able to "mount" your hard drive(s) and look for the file that you need to fix.
mounting makes the drive partition available to the linux system. the command will be something along the lines of "mount /dev/hda1 /mnt/hd" where hda1 = the hard drive you installed Slackware on.