Widget puzzle

I’m trying to design a child theme, based off of twentytwelve, and I’m running into a puzzle I can’t even figure out how to troubleshoot.

Basically, my theme explodes when I enable any widgets.

I’d be happy to troubleshoot this on my own, except that I’ve already commented out <?php get_sidebar(); ?>. I’m not calling any widgets. How can uncalled-for widgets do anything? I’m totally stumped.

I’ve tried checking out the HTML that’s generated, and the broken version has identical source code to the working version, it’s calling the same stylesheets, and I have no idea what else to look at. Any ideas?