5GB website - issues in backup while transferring

Hey,
I have a website on one server which is a social network with about 5GB worth of data. When I create a full cPanel backup in order to move it to another server, for some reason, it wouldn't backup "home dir" files.

When I restore, I see the database etc restored properly, but there are not files within public_html. I also tried downloading/uploading these files simply through FTP but it breaks the site [even after re-checking database configuration files].

Do you have any idea what should be the next step?