Zvit, thanks for your kind offer. After several hours spent trying to set up the Airport Extreme, I finally succeeded! I checked many requests and responses in Windows7Forums regarding the issue, as well as references in Apple Support. The Airport managed to find a connection when wired to my Netgear router, as well as when wired to my new Dell XPS laptop, but no wireless connection could be found. The Airport Utility was not much help either. It found the Airport when wired to it, and I was able to do a factory reset and then go through the set up procedures as instructed by the Airport Utility. When it came to making a wireless connection, however, The Airport Utility kept saying it could not find the Airport! I spent further frustrating hours searching for a solution.
I decided to rule out anything internal, so I went to my Control Panel (Windows 7 Home Premium), and checked potential sources. I looked at Hardware & Sound/View Devices and also Add Device. I wired the Airport to my Dell, added it, disconnected the cable and then tried Network & Internet/View Network Status to see if it showed. Hey presto, there it was! Marvellous! Green light showing on the Airport, even when wireless, thus "proving" the connection. I then went back to Airport Utility, and it once more refused to “see” the Airport. Since I knew it was actually connected, I disregarded the Airport Utility and simply tried opening Firefox/Google and made a wireless internet connection no problem.
I tried opening Airport Utility again just now, 1 day later, and Airport Utility has “found” the Airport and says I have a wireless network. Well I am surprised!
The moral of the story is that there is sometimes a simple solution that no-one has encountered before. Also, do not give up, there must be a solution, even if you haven’t found it yet!