Thanks for all the replies on this thread. This morning, after about a week of doing nothing with this problem due to lack of time, the SoundBridge magically appeared in "My Network Places" and the laptop advised me about this upon powering up with a new (and unfamiliar) icon in the system tray, advising that a new network device was available. At first, it showed 2 new network devices, one being the SoundBridge and the other being a new D-Link DI-series router (I have a D-Link DI-824VUP router). But then, that second icon just disappeared for the DI-series router, leaving just the SoundBridge.
Even though the SoundBridge has been working fine otherwise all week, the computer has been acting funny through this time, in terms of Norton Internet Security asking for permission for all sorts of things, and also in terms of the icons on my system tray not appearing as they usually do, for those that I have set for "Always Show." Some of those icons are still not there, and I have been manually re-setting the "Always Show" command for some of these, which has been bringing some of them back.
I'm convinced that the problem with the SoundBridge not appearing under "My Network Places" has been associated with Norton Internet Security. Once It finally got a rule made for itself that it was okay to allow the SoundBridge to appear (through my repeated "permitting" of all sorts of Norton popups), it finally allowed the new device to appear. We'll see if it stays there.
Don't know about the mystery of the disappearing system tray icons, unless the computer was working hard this week to figure out how to put that new icon there, and it was otherwise disrupting the normal icons - I'll have to fool with that some more.
Maybe this will help someone else with the same problem...