So the really strange thing is that no contact forms seem to be working on my site... I've tried Visual Form Builder, Contact Form 7, Contact Form Manager, and Easy Contact Forms, and none of them seem to work.
Easy Contact Forms is the only one that actually gave me an error. It said "error. status=0" which according to their support page usually indicates that "the site domain names in WP Settings Word Press Address (URL) and Site Address (URL) fields are different." I checked, and they're not.
I've seen that a lot of other people having trouble with contact forms are having trouble due to the server not sending the email, and so I tried the common solution, which is installing the WP-Mail-SMTP plugin. I set that up and sent a test message, and the email was delivered correctly. So the problem is not due to that...
Any more ideas? We really need to be able to have working contact forms, including with the ability to upload files.