Ok I did what Jam said, changed where it saves to, to the Desktop, then tried downloading a test file and it still didn't work. I then searched for the exact thing that I had downloaded and it was nowhere to be found on my C Drive. I even checked the little download box that Firefox has for the files, right clicked what it had TOLD me it downloaded and tried to click Open and Open Containing Folder, but those options were whited out.

Surely this means that contrary to what you said, Thaylok, the download just isn't working? It can't even be the thing I'm downloading that's the problem because I've tried to download all sorts of different types of file to see if that was the problem.