It turns out that my computer ran the checkdisk utility after I restarted it. It was able to repair everything that went wrong with F: and I don't have anything that's lost. This made the horrible feeling in my stomach go away, but I don't think it changes the fact that I don't want to purchase any more Microsoft products.
I think I might write a program on my Ubuntu computer that automatically backs up all the important stuff once a week. I should be more vigilant in doing this on my Windows machine, but having to do it manually and waiting forever for it to work is not what I'd call making it easy.