Hi Mark,
Yes, it had finished indexing, but you gave me an idea. This was with a large project. I opened a smaller one, and the Search function was enabled and working OK.
So, I trashed the Media Cache in the larger project where Search was MIA, and... still no luck.
But, I started trashing unused items, and then remembered "Edit>Remove Unused," and that brought the Search box back. So, it appears that some Project item was causing Project Search to be disabled.
So, let's consider this question answered. Thanks, Mark and Kevin.
Jim