I signed up with a new hosting company, and CF7/RSC give this error:
This contact form contains CAPTCHA fields, but the necessary libraries (GD and FreeType) are not available on your server.
Both libraries are installed and enabled. I have found other instances on the web where people are having the exact same problem.
In light of my own Linux experience, I suspect the problem is related to version numbers of one or more libraries.
I have found no solution to this on the web and am now going to start looking for another captcha plugin. I hope I can continue to use CF7.