if you can boot with the boot disk and everything else is normal, then it sounds like a problem with your boot loader. when you installed slackware, did you tell it to install LILO, and if so where? the default is to install it on the MBR, but you can also choose another location. i highly recommend installing LILO to the MBR, i've always one it that way and it's very safe, very easy to make changes, etc.
use the boot disk to boot up, then log in and check the contents of /etc/lilo.conf. please post them here. that may help us work toward a solution.