Please no, "I don't know" or stupid responses.
When you do this, you can literally copy and paste all the old files from the old server to the new server, then import the sql file, and, after making some modifications to the config files in order to accomodate the new mysql server, it'll be the exact same forum. If this is what you want, that is.
If you don't have access to the db, there's not much you can do.