If you stop the MySQL server, tar up the directory holding the database files and copy it to your new server you should be able to just untar it in the proper location (differs depending on how you have it set up) and start the server on the new system. However, if you can't access it on the original server due to user/password issues, you won't be able to on the new server without fixing those issues as well.
HTH
Forrest
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