I take it you copied and pasted these lines from dmesg or something. As they appear in that order I'd think that the dhcp broadcast is sent before the ethernet interface is brought up.
To see if that really is the problem you could try to login and restart the dhcp client (/etc/init.d/dhcp restart on my system but I seem to recall that slackware keeps the init scripts somewhere else). Then a new broadcast should be sent out but this time the ethernet interface is actually up. If this works you should move the starting of the dhcp client to the end of the init procedure after eth0 is up and running.
Hope thie helps.