Slackware has a kernel named 'bareacpi.i', which has ACPI support compiled in. However, you'll want to check whether this kernel supports your sata chipset or not.
The easiest way is to try booting from the Slackware CD1, using the 'bareacpi.i' kernel.
Once you're in, find out if Slackware can see your hard drive's by doing:
If it can see your disk/partitions, then just install the bareacpi.i kernel, which has the ACPI you want.
If not, then make sure you have kernel-source package installed. Then do:
cp /boot/config /usr/src/linux/.config
cd /usr/src/linux
make menuconfig
And enable ACPI - and compile/install the new kernel. I won't go into details since there's so many threads on how to compile a Slack kernel properly.
Copying /boot/config will allow you to start with all the pre-selected options from your current kernel, and go from there. This is easier than starting from scratch.