After getting comments from people who still use Google Friend Connect to read blogs, I did a little checking. It seems Google, in their infinite wisdom, no longer put the widget in their list of gadgets for Blogger. Maybe that says something about their future plans...
But there are so many clever people on the web, and they contribute to forums, and they figure out the code so I don't have to!
In my sidebar I've now got a gadget for GFC. It doesn't have the usual graphic, but it's clearly labeled. And it works! Thanks, Sheila, for testing it!