That was it! The theme is the problem. I also got this message when I switched back to the theme:
Attention:
We've detected that the JetPack Plugin is currently installed.
If you wish to use Sterling's built-in Form Builder you will first need to disable the JetPack Contact Form, Publicize, and Sharing Modules.
I guess I've reached a dead end. I seriously doubt if my client will agree to change themes.