Ok, I know the reason why I'm not seeing the list of connected devices. My primary computer (that I'm using right now to access this forum and type these posts) is Windows 98. My browser is Firefox version 2.
When I access the web menu for the 605L router using FF 2, everything looks ok (page formatting, etc). I can seem to do everything just fine to interact with the router. But this one place (show connected devices) doesn't display anything.
On another computer (running a newer version of FF) *DOES* show the list of connected devices!
So I went back to my Win-98 computer and tried Opera version 12 (a much newer browser compared to FF 2). There is a problem with Opera 12 that prevents it from even showing the login screen for the 605 router, but I got around that by pasting in the entire URL from the Firefox URL. And I see that yes, Opera 12 also DOES show the list of connected devices.
So when interacting with the 605L router using a browser, everything seems to work ok using Firefox 2 except for showing the list of connected devices. When using Opera 12.02, Opera can't even access the login screen correctly because it is re-directed to "http://(null)/index.html"