I'm replying to the original post as I am referencing multiple suggestions here.
Ian Broad
Doing what you suggested above did indeed allow me to pull "python" and "import" through the command window, but it didn't fix the issue I am having with the add-in.
I restarted my machine, re-created/re-installed an add-in with one toolbar that had one button, added a MessageBox command to the onClick function...and I still get a button that says missing whenever I open up ArcMap.
Rebecca Strauch
I was looking at my XML config file, and I noticed that my target version was set to 10.1. Whenever I was working in the 10.2.2 yesterday, my target version was 10.2, but now that I'm in 10.3.1, my target version says 10.1. Very confusing. I changed the 10.1 to 10.3.1, and in doing so, the add-in will not show up in ArcMap when I open the document. It says it installed correctly, but it just doesn't show up. I changed it back to 10.1 and it shows up again with a missing button.
Is there some sort of issue with that version number that could be causing problems?