I uninstalled jetpack and things started to work again. I had already got to Discussion settings in order to try and fix the problem. As soon as I uninstalled Jetpack, the comments started showing up on my blog agin.
I should also note that I can see the comment boxes when I am logged into wordpress. But if I look at my website from outside of wordpress, or if anyone else looks at the blog, then the comment box does not show up.