Thanks for your help jpretorius.
Well, All the cables and ports are working just fine. That was the first thing I checked.
I did check the IP addresses on the 2 computers that work,
and their IP addresses ARE DIFFERENT.
In discussing this ordeal with a friend of mine, he seems to think that I may need
to reset the IP address to work with the router for Computer A being that this
IP address was originally setup to work with the
connection coming directly out of the modem. (as indicated in Hook-Up #1)
What Is Your Take On This???