Download Parted Magic here:
and use the included gparted application to check out your partitions on that hard drive. I'm guessing there is a hidden diagnostic or recovery partition on the hard drive, as most Compaq's come with one. Whatever you find, try deleting all partitions and then repartition with one large ext4 partition which will hold your Slack install and one small swap partition. When you do the installation, use these existing partitions designating your large ext4 partition as being mounted on "/".
9GB should be more than enough for a standard Slackware install. If there isn't a hidden recovery partition on there, you may not be using the partitioning utilities available in the Slackware installation routine correctly - they can be pretty confusing if you're not used to them. By setting up your partitioning scheme in advance using Parted Magic/gparted, things go easier and you can be sure you have your partitions right.