Beware: If you are logged in in your browser as a facebook page, this widget will not show up.
You can test that by going here:
If in the sidebar you see just four empty boxes with these titles...
Thin Like Box. Minimum 181px
Like Button Only
... then you are very likely logged in as a page in your browser.
Switch to your fb profile and the widget will show up in the sidebar.
This is the reason why many people say it doesn't work for them in browser X but it works in browser Y. They are just not logged in in each browser or use each with a different ID (profile vs. page)
Not sure if this is normal for any fb plugin in WP (didn't try others) or if this is a bug in this particular one. I know e.g. news websites (their comment sections) that work when you use fb as a page and some who work only when you use fb as a profile so they give you the option to switch your identity. This particular plugin won't give you the option and just won't show up.