That error means that the physical disk space on the data store (the storage area network that you are sharing with all of the other users on your server) is nearly out of space. cPanel and FTP operations are suspended when that happens in order to prevent corruption of your data. It has nothing to do with your account. It will take at least an admin with unrestricted file system access to fix the problem (clearing temporary/log files or perhaps even closing abusive accounts), so you'll just have to be patient.