Not sure if you’ve figured out this problem by now or not.
first off, this is not support - this is a support forum populated with other customers like your self. If you want to contact support, please do that through the Web Control Panel > Support > Contact support
Seconed, my sigguestiosn would be to clear the data out of the database, make sure the language is set to the same as you were using with your previous host, and then try dumping it in there again. Possibly if the language was not set right, mysql would not know what to do with the charcters it was getting, so replaced them with ???, rather than keeping the actual data.