First question is really a two parter:

Part1: Why is it that when I boot into text i can run ifconfig to get my broadband address, but after I startx, then logout, and type infconfig again, it doesn't read it as a command? Just gives me a not recognizable error? I have to reboot to find out the address again..

Part2: Why is it that after a while the eth0 address changes? I thought it was supposed to be steady until the link goes down?

Second question: Why does gnome quit working after a while? For example, after a while from keyboard, I come back and click on an icon such as a terminal to execute a terminal, it gives me nothing. In other words, none of the programs work. Is this common?

Thanks to LinuxQuestions for Answers!

i think you need to do a google search for linux
ethernet howto, or linux cable modem howto.
that will have the most stuff for you to try in one place.

The answer to part two may be that your using DHCP and your touter is set to renew the address often. I would just use a static IP which can be configure by typing "netconfig".
I'm not sure about the answers to part 1 and question 2.

More information about the hardware you are running on would be helpful to answer question 2.

Dual boot on two separate drives, Linux being on it's own 4 gig drive. (don't laugh)
450 mhz AMD k-6
256 ram
standard ethernet card
redhat 8.0