When I install Slackware 7.1 on my machine, do I also need to install Samba in order to logon to a NT server on a network? Or can I configure my system normally for a TCP/IP network connection? They also use a DHCP server.

You would need samba to connect to an NT share.

Could I still access the Internet by logging on to the NT server without Samba. I'm not really looking to access any of the shared resources on the network, just access the Internt. By the way this is on a college network.

You would need some kind of proxy software on the NT machine so you could use it as a gateway. I would recommend using the Linux machine as a gateway and having the NT machine access the Internet through the Linux machine.