Again, thanks for all the thoughtful suggestions. Although when the drive originally worked, I was running my normal computer setup, I now have only mouse and keyboard USB plugged in, and there's not much else connected other than the normal network and monitor stuff. In response to a suggestion, I also uninstalled my CD emulation software as well.
I also downloaded and ran the UVCview software suggested but it is not clear to me how to report its results. It allows me to save a .txt file which seems blank -- how do I upload the results?
I decided to take a little Hitchhikers-Guide-to-the-Galaxy tour through the suggested troubleshooting software step by step. Here it is - pour yourself a cup of coffee. 
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Under Troubleshooting Assistance:
External Drive Troubleshooters:
Windows 7 & Vista:
Check the Power Cable -- check
Check the Data Cable -- check
Check the Partition and Format Status Using Disk Management -- click
"New Installation" or "Previously Working" - well, I guess I should select the latter -- click
Now I navigate as directed to Disk Management
Suggests here that I "become familiar with the drive letters and partitions." -- OK
Describes what reference I should see for the GoFlex (drive letter, capacity and type of partition, show drive as healthy) and provides and example.
What I see looks nothing like the example. I see:
(a) 3 Volumes associated with my C: drive shown as "Disk 0"
(b) Removable Disks 1 through 4 (F:, G:, H:, L (no media)
(c) CD-ROM 0 through 3 (D:, I:,J:, K (no media)
On to page 2:
First step is to "Check the upper window to find whether the drive letter is present." In my case it is not. Thus the rest of the page does not seem relevant.
On to page 3:
Page 3 speaks to data recovery and corrupted partitions. Not relevant to me since I have no references to the GoFlex whatever.
On to page 4: Speaks to reformatting the drive. Again, not relevant to me since I have no way to address the GoFlex.
On to next subsection: "Check the Drive's Status Using Device Manager":
Select "Previously Working"
Under "Check Drive Status: Previous Installation" I am now asked whether I have:
(1) a GoFlex, GoFlex Pro, or GoFlex Desk with USB 3.0 or
(2) a GoFlex or GoFlex Pro with eSATA
This is a bit confusing. I have a GoFlex Desk with (I presume) USB 2.0. Does the GoFlex in (1) mean all GoFlex's or all GoFlex's with USB 3.0? That is, does the "with USB 3.0 refer only to the GoFlex Desk or does it refer to all 3 models listed?
Since GoFlex also shows up in (2) I'm assuming these two paragraphs ares for USB 3.0 and eSata installations only and am guessing that neither are relevant for me.
On to the last paragraph on page 1: "Checking Drive Status in Device Manager":
Click on Windows symbol, right-click on Computer and choose Manage. --- done
On to page 2 where I'm asked to select Device Manager and observe what is listed under "Disk Drives". What I see are 4 generic usb devices and my C: drive as listed in my previous post.
If the drive's model number/name is there, I'm told to try the drive on another computer. Of course the drive's model number/name is NOT there.
If the drive's model number/name is not there, I'm told to look under "Other devices". I no longer have a category named "other devices" since I uninstalled my CD emulation software as suggested.
Not much seems relevant until I get to last paragraph on page 3, having to do with searching for "C:\windows\system32\driverstor" and then on page 4 am instructed to delete "infcache.1" and some tips on how to overcome the operating systems objections to my doing that. Speedreading a little further down the page I see where I may have to haul out my Windows install CD, do a repair/restore and, it states it might be a good idea to backup my data before I do this.
Well duh... we've come full circle. I can't back up my data because I can't get the friggin external drive to work, and it is the thing that's leading me down this path in the first place.
I'm sorry, there's a limit to how much mucking around the OS I can justify for troubleshooting purposes, given the range of inexpensive external drives out there, and I'm not excited at compromising what has been an absolutely bulletproof computer setup to date. I appreciate the thoughtful help I've been getting on the forum, but the drive is beginning to seem a bit fussy for me to be confident that it will be available if/when the time comes that I'll actually need it to appear and restore my data.
Finally, on page 5, it says to try the drive on another computer and if the same problem is there, there is increased chance the problem is with the drive. It seems to me that should have been Step 1 on page 1 before one plows through all the above. As already stated, I have the identical symptoms on my other two XP computers.
Thanks again for slogging through all this with me -- if any of the above suggests a possible solution without dissassembling the OS, I'm more than willing to try it.
-- Mike
