Boot messages will not be logged to file as long as the syslog daemon has not been started (which is after the filesystems have been mounted).
So, the first part of the boot messages is only seen on the console. If you want to know what was on the screen before it scrolled off the top, try using the <Shift><PageUp> key combination to scroll back in the terminal buffer.
If you run a default Slackware (i.e. vesa console, and not booting directly into X) then this will work.