Just to share my experience. I moved a site from godaddy to a hostgator cpanel, and in so doing ran into a problem importing the database - I got a MySQL error #1044 Access denied. After an hour and half with HostGator tech support helping me, I am not quite sure how but it finally imported and now the site is up.

It seems that the problem may have a conflict in the naming convensions of the database - that is that database names in HostGator require a prefix of the username of the cpanel, ie username_databasename - and when importing the database via PHPmyAdmin, it was trying to create a database by the name given to the database when it was created in the Godaddy hosting account, which could not work.

I think the tech support ended up moving the database in via another route, possibly via root access? Not sure. Just thought I would put this out there. Sorry I don't have more for it.