Restore MySQL Databases from File backups, not MySQL Export

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http://serverfault.com – I've got a Windows Server and I get Windows Server Backup to backup all the files every day. I don't however have a system image so I cannot use that. I've tried just copying the database files into the MySQL Data folder, but most/all of the tables are missing (wordpress). Is there any other way I could recover this data? I believe it was using InnoDB. (HowTos)