Try using the command "netconfig" as root -- that's the Slackware network setup tool.
Can you ping LQ.org? Try the following commands and see what the response is:
$ ping linuxquestions.org
$ ping 220.127.116.11
If you get a response for the second and not the first, it's a DNS problem (search the Slackwae forum for how to set that up). Else, there's ... something else wrong