Not mine though. I have got LOTS of space…
EDIT: Somehow weirdly solved it… First of all, I switched to 4-collumn view on the Dashboard, and switched on everything possible. Then I moved stuff around and closed the screen options. I have noticed there is a “Recent drafts” thing – I clicked one auto-saved (which I could not submit because of no “publish” button) and – THE SIDEBAR APPEARED! Hurrah!
This however does not appear with “New Post”, and the editor is still going all weird. (switching to “HTML” shows the visual controls, switching to “Visual” hides them… O.o)