I discovered the problem finally, after nearly 6 months of looking for it.
I am using Norton Internet Security, on all of my machines, that I downloaded from the ATT website. Well, it turns out that on all of the wireless machines, Norton blocked file sharing, browsing the network and various other settings when the access point was connected to the system. Apparently the software thought the new access point was a security threat and blocked its access automatically.
Accessing the General Rules in the Advanced Settings under the Personal Firewall area of the configuration in Norton, allowed me to reset all of the blocked services and restore the connection. Unfortunately, I had to perform the functions on each of the wireless machines (again, none of wired machines were affected) to restore service completely. As I reset each machine, I was able to access a greater portion of the network.
This was a very difficult nut to crack. I kept thinking that the problem was a firewall, but didn't do much looking at Norton, thinking that since it worked correctly on another access point, that it couldn't be the problem. Obviously I was wrong in that assumption.
I hope this post may help others with similar problems.