Mine was gone too (Chrome), then I noticed at the top in the browser saying something like "blocking unsafe scripts". I clicked on it to re-enable the scripts and now the google search box is back.
Here is what I clicked on, it looked like a shield w/ a red x on it.
google chrome - Undo allow loading scripts over HTTP in HTTPS page - Super User
However, I can't seem to find a way to undo this to see if that is what fixed it. Clearing cache and restarting Chrome didn't do it.