Anyway I talked to my dad and he said all I could do is take it apart and see if there's anything jammed inside it. Please note that he told me to do this. I think that information is important now that it doesn't work at all. Whoops.
So I saved the essay onto my memory stick and have just printed it out at uni. Yay. This is the first time I've used the memory stick with one of the uni computers so I'm pleased it worked and didn't decide to join the technological conspiracy against me. And now, disaster averted. (Because I am the kind of person who sees not having my essay done on time a disaster...I panic when I think I might be a few minutes late for class!)
Of course the good part about all this is that the worry about whether or not I'd actually have an essay to hand in has overshadowed the worry that it's complete shit.