A serial mouse (we assume Microsoft 2 button type here) has to be powered by the serial port to send data to the host. Also the parameters of the serial port have to be setup correctly (1200 bps 7E1), so the cat /dev/ttyS0
trick will never work.
Fortunately Slackware already includes a program, which does everything we need. Just do:
# /usr/sbin/gpm -m /dev/ttyS0 -t ms
Then try moving the mouse. You should see a moving rectangle (the mouse cursor).