On Friday I spent over an hour trying to fix my Firefox tabs - I could no longer drag them to reorder or to a new window, and ctrl-shift-T didn't restore tabs, but I could still do it via menus. I thought it might be something to do with the new tab-island stuff and tried FF safe mode, restarting computer, confirming about:config options, etc.
Turns out my headphones were resting on my Esc key.