I am running TopologiLinux which is a distro of slack. I am a complete newbie and dont know how to configure it to use the internet. I am running KDE GUI

What means are you using to try to connect? A USB cable modem? An Ethernet one? A Router? ICS?
I know that if it's going through a router with dhcp and your ethernet card is detected, you can just type (in the terminal window)
ifconfig -a
and then
dhcpcd
and you should be in business.
I just need some details on your hardware configuration in order to provide much more help.

Wut ? TopologilLinux is a distro of slack ? No idea ..

I've Motorola Surfboard SB4200i connected through a cat5 to my DLink 538TX NIC on a pci on mobo. I got hooked on the immediately by first booting after installation of slack 9.

U need just to give some information during the installation configuration of slack correctly ..

If u r trying to figure out wut wrong the start point is maybe to have some look into the script in /etc/rc.d, check whehter script u possibly needed for .. have execute permission (rwxr-xr-x), also check their content, Am not in slack currently can not point exactly which files ..

As mentioned above u should write in more info to get advice from the profis ..