I found the solution to my query.
First thing I did to resolve the problem was to test if the problem was unique to my profile (logon).
It was. I set up a Temporary Profile and didn't have a similar problem.
I checked the registry and didn't find any double entries for COMPUTER.
So, then instead of clicking on Windows Explorer on the Taskbar, I clicked on the one that's found in Start\All Programs\Accessories. When that opened, there was only one COMPUTER listing for all my drives.
Somehow the link for Windows Explorer on the Taskbar had become fouled. So I unpinned it from the Taskbar, made a shortcut of the link under Accessories and then put that one in the Taskbar and my problem is resolved.
I hope this will help someone else with the same problem.
Your solution solved the same problem on my Win7 Professional 32bit system. Taskbar launch of Windows Explorer seems to be the culprit, unpinning and replacing seems to work for now.
Wonder if this is related to the frequent instances of deleted files remaining displayed in the folder list pane with Windows Explorer? Certainly that after 20 years, Microsoft could get Windows to accurately display the presence or absence of files in a directory.