First off let me thank everyone for their help.
I was able to solve the problem in five minutes.
The system is now running correctly. I'm able to gain internet access
from any work station on the lan. Still don't have e-mail or ftp, but
that's a fire wall problem that will be worked out tomorrow.

What fixed the problem, you ask??

Brian Densmore, hit it right on the head. Charles Steinkuehler and
Jonathan Hutchins were alluding to it. I had the same network address to
both sides of the linux box i.e. 192.168.0.101 and 192.168.0.1.. After
changing the outbound cards address to, 192.168.1.101, (and the routers
address, 192.168.1.135) everything works fine.

The question that I now have is, WHY did the Caldera's OS work properly
with the old ip address set up and RedHat didn't???

Jonathan Hutchins stated:
"We know it's not an IP Address question, because it worked under your
other 
distro, so it's got to be something about how RedHat is starting the
network".
And "If necessary, we can step through the boot process and figure out
where it's 
going wrong".
Jonathan, I would like to follow up this. I can easily change the
setting back and go through the start up routine. 
Just tell what you want to know.

Thanks agine to all for your help.
Doug