I just setup this slack box and ran my netconfig. I am on a shared cable modem connection (switch) with ip addresses from a dhcp server at my ISP. When run "ifconfig eth0", there is no line specifying the ip address (the inet addr: field). It looks similar to this:

Link encap:Ethernet HWaddr 00:50:FC:4C:B6:51
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:39080 errors:0 dropped:0 overruns:0 frame:0
TX packets:20737 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:100
RX bytes:56575180 (53.9 MiB) TX bytes:1424432 (1.3 MiB)
Interrupt:11 Base address:0xfc00

Am I missing something? I at this point I am not able to access the internet. This is the first time I have had two computers running and networked. Thank you in advance!!

you most likely need to specify that you want that certain interface to utilize DHCP...

I am not familiar with slackware so I cannot comment on exactly how this is done. I know that on my RedHat boxes I would edit /etc/sysconfig/network-scripts/ifcfg-eth0 and set the "BOOTPROTO" variable to "dhcp".

Also, have you purchased another IP address?

Do I have to purchase a second ip? My cable connection is split by a Linksys 5 port switch (not router). Not sure how this works, I figured that the second computer would be assigned a dynamic address just like the first computer I set up.

My first machine was a windows box that I've had since college, and have since created a partition w/ Redhat and then Slackware 9.1. When I start that machine, the dhcp worked fine, without having to change the script. I am not too keen on assigning ips, when to use static ips and what the isp allows. The only internal network ip that I use is the loopback.

If you want two public ip's you need to pay your isp for that, then it should workwith just a switch. Right now, your isp will ignore the second box.
You're going to need a router if you only want one routable(public) ip.
With a router, the isp's DHCP assigns a routable ip to the WAN port on your router. The router's DCHP assigns private ip addresses to your machines, then a feature called NAT let's you split your one public ip for your machines to both use. The NAT router also adds another level of security to your network.

Thank you Rhell, I am beginning to read up on this. Looks like I could just setup another linux box to be my router/firewall, then switch the connection from there. I guess I now would need a second network card for the Routing machine??

Yep.