My Slack tower is fixed.
The root cause was that, somehow, when I created a new partition from some free space on the drive, the Slack install didn't like it one bit and complained the whole time. I'm not going to blame Gparted, though...
On this system, I use / to house the whole Slackware install, using /home as a directory instead of having it as its own partition. /home was 9+ GB and growing, so that / was at 92% in utilization. I decided to move it to its own partition. Using Gparted, I created a partition (/dev/hdb5). There were currently two primary partitions already on the drive (/ and swap), so I decided to create a logical partition to house /home. Somehow, Gparted fux0red the extended partition, I think.
Soon after I created the partition, I began to see boot errors hinting that there was a corruption problem with this drive, although if I sat through the boot errors, they'd finally stop and I'd get a login prompt.
I misdiagnosed the issue and thought that this 7-year-old drive had finally gave up the ghost. I almost trashed the drive but decided to give it another shot by removing the extended partition and making a new partition, a primary one. In fact, I made two and move /home to one of them (/dev/hdb2, I believe). Afterward, I adjusted my /etc/fstab to see /home and rebooted. There were no more errors on boot.
Next, I need to start doing nightly/weekly backups (somehow), then maybe clear out my /home and get rid of some junk (maybe backup to DVD).