The blank page is probably a continuing problem with the cPanel "Basic" theme; if you're over your quota, you won't get a working cPanel page. The error you're seeing over FTP is probably the real deal (I don't have server access to your account, and can't check for you). Unless you have requested and been granted an upgrade to umetered storage, you are allowed either 512MB or 1GB of storage space (depending on the account set-up), and will not be allowed to upload more. You may want to check things like your error logs and email directories if you're sure that you haven't uploaded enough files to fill your account space — script problems and such can add a lot when you're not looking. And look for site backups, which may be getting created automatically, download the latest, and delete the rest.
If you are still finding yourself short of space, you may want to request an upgrade by following
the instructions in this thread.