Thank you for your replies.
Yes, I heard about some hosts who will do server to server transfers. Unfortunately, that wouldn't work for me because my former host wouldn't allow me to access my site anymore. My pc crashed, and it had my login info on it. And because my former host and I had a disagreement, it wouldn't provide me with that info when I requested it. Lucky for me, I had true fans who kept signing up even though I hadn't updated my site in months.
Having said that, it seems I will have to stick with the FTP process. So HomerSimpson hit the nail on the head, and my former host put the nail in my site's coffin.