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unless you actually have a dump of the MySQL db, then there is no recovery.
or if they haven't deleted that actual db from that particular server maybe they could do a dump or transfer for you either by mysqldump or by copying/moving the MySQL files for that db from the /var/lib/mysql/<db name/ directory on the server itself and then create you a db of the same name and transfer all those .MYI, .MYD, & .frm files etc to your new server..
but if they can't then, i'm afraid it looks like u gotta start again or use your last known backup if u have 1.
files are unimportant to the db itself.. you can reuse them, but if u haven't actually got the sql dump/backup your db is lost.