On another site I have, I had changed the front page to a static front page and noticed the sidebar was missing. I didn't really mind much but finally got around to fixing it. I did an inordinate amount of digging, but finally found this WordPress forum topic that asked the same question.
The answer is simple: change the template for the static page to one that includes sidebars. I'm using a child theme of Twenty-Eleven so the page has a default template of "Default Template", but by switching it to "Sidebar Template", the sidebars appeared.
And here I was digging around in the PHP code to try and find out how to do it. Nonetheless, given how much out-of-date and mis– information there is out there, I thought I'd go ahead and make this post to hopefully save someone else the trouble.