I reviewed the Twenty Eleven 1.4 theme in my own Wordpress site (which is updated to the latest version) and I added a Side bar per the Widgets and it appears. You would need to go to Widgets and drag the CATEGORY widget to appear in the sidebar for it to show on your page. If you only posted in Categories and did not complete that step, then side bar would not show. Note that you need to have posts that are ASSIGNED to that category in order for the category to show. Otherwise, it won't show up.
I unfortunately cannot access the information you shared in chat with live support, but if you wish to have this issue reviewed further, we would need to be able to login to your dashboard and take a look at what you did. If you want us to do so, please email firstname.lastname@example.org after setting up a temporary administrator user that we can use to login to your Dashboard. Make sure your email is titled COMMUNITY SUPPORT- Wordpress Help. So that we can find the email.
Do not indicate your account information in your reply to this post. We can see that information here. Hopefully, the information I have shared will be enough get you going with the categories in the sidebar.
If you have any further questions, please contact technical support or leave a comment at the bottom of the page.
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