I activated the original theme and the issue did not persist. So it must me something in my child then, right? I took some screenshots and put them up on my site here.
The first photo is what the screen looks like when you click on the word "menu" with the twenty twelve theme activated with no modifications. All the menu items show up in a list. The second photo is what is looks like with my child theme activated. Clicking on the "menu" button does nothing. Also, it seems that the icons at the top of the screen are all missing with the child theme active.