Got it figured out. I found this posted yesterday about the newest 2.4.x kernel:
http://lkml.org/lkml/2007/7/22/160 Armed with this information, I was able to get it working. Here's how:
I booted from test26.s off a USB drive, partitioned the hard drive, then started the setup program and installed from the 10.2 CDs. I picked bare.i, knowing that it wouldn't work. After installation, I rebooted, again booting from the usb drive with 'test26.s root=/dev/sda2 noinitrd ro' as the boot string. (This loaded the 2.6 kernel that recognized the SATA controller and told it that the root file system exists on /dev/sda2.)
I got a prompt and extracted the 2.4.34 kernel to /usr/src. I then applied the patch to take the kernel to 204.35-rc1. Compiled the kernel, installed it, rebooted, and all was well.
I really wish that Slackware would be updated with the 2.4.x kernel, but I honestly expected a move to 2.6 before this.