I've never had a problem with a PS/2 kbd. With USB, yes; PS/2, never.
When you first boot, go into your BIOS and check the settings for anything related to keyboard, and PS/2.
Boot with the Slackware install CD1 and at the boot prompt enter:
hugesmp.s root=/dev/hdc2 rdinitr= ro
which should get you into your Slackware system. Then you can see what modules the PS/2 mouse is using.
You'll need a USB flash disk, or a shared drive (which I assume you have since you say Slackware is on hdc2), where you can copy this output to later post in your thread here.
We need to see the output of the following commands:
Probably the easiest way to see what the kernel is doing with the kbd is this. Open a terminal, and as root issue "tail -f /var/log/messages" then unplug your kbd. Look at the messages that appear in that terminal, then plug the kbd back in. It will output what the kernel does, what modules it loads, to support the kbd. You can then copy and paste that output to here, also.