I started this thread with a question, but along the way of retracing my steps, I figured out the answer! Since someone else may encounter the same problem, I thought I'd share.
I just upgraded from a Motorola Cliq to a Samsung Galaxy S (T959) this week and am trying to get it set up with my info from my previous Android phone.
I had previously been successfully using an app/software called Wondershare MobileGo to backup and manage my phone's contacts, pics, music, etc.
When I connect my SGS to my laptop via USB, the MobileGo program automatically recognizes the phone and cues me to start the connection process. This requires going into my phone's Settings > Applications > Development , then selecting USB Debugging.
(With my previous phone, I would connect via USB, change the settings on the phone and then all would go smoothly from there on.)
But now, when I do this, I get a pop-up on my SGS saying "Attention - USB is connected. Remove the Cable." with only an OK option button.
If I leave that alert up on my phone and cue the laptop software to proceed, it then proceeds to install the SGS driver on my laptop and then deadends after awhile and starts over.
The SOLUTION is quite simple. I have to go through the steps on my phone to enable USB Debugging mode BEFORE I connect it to the computer with the USB cable. If I do that first, then connect, all works fine.