When you get a kernal panic you should be able to log into your system (using the boot floppy that you should have created when installing the system) as root. If you have not created a boot floppy you might not be able to
Once in as root if you look at the error messages & stuff you should be able to repair the problem - in theory.
Unfortunately in the past i've had a problem like this that was due to faulty installation media. The curruption to the system was too complex for me to understand & fix so I just re-installed with a new distro..
Im sorry to sound negative, but im sure someone might be able to give you a few positive pointers on how to fix this. How about looking in the slackware section? you might get some helpful tips there.