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i was under the impression that blocks are stored in the database, when created from admin. someone please correct me if i'm wrong
as for restoring your site, you've pretty much lost everything if you can't get your database from your host. if you can't get a response from them, you'll have to upload your files from your old site to your new host, delete mainfile.php, copy mainfile.dist.php to mainfile.php, and install from scratch
you might also have to delete the files in the cache folder, but i'm not sure
hopefully someone else more familiar with reinstalling will give their advice