Did it detect your card? Giving a domain shouldn't keep you from getting internet access. These are the steps it should ask:
1. Hostname: Basically what you want the name of your computer to be.
2. Domain: If you dont know, just put your ISP's name there, like for example if you use earthlink, use earthlink.net
3. DHCP or Static: If you select DHCP, it should automatically assign all your addresses like IP, Netmask, and so on but usually it won't get your DNS entries so you need to add your ISP's DNS servers in your /etc/resolv.conf file in this format:
Where the 000.000.000.000 is the actual IP address of the DNS server and spell out nameserver. Some will actually put:
At the top, to search your ISP's domain, that would be for example like earthlink.net, etc.
4. If your using Static, you will have to specify all your addresses like IP assigned to you, Netmask, Gateway.. etc.
5. If you have it so Slack tries to probe for you card, if its successful, it should setup your /etc/rc.d/rc.netdevice file to automatically insmod your correct driver for you module to be used for the NIC. If it didn't find your card, you might have to recompile your kernel or download drivers to support the card. As far as I know, your card should be supported, from what I recall, should use the sis900 module.
Let me know if any of this helps you out getting online.