CiviCRM Wordpress Migration: Stumped by the Database
There is some documentation here that should help: https://docs.civicrm.org/sysadmin/en/latest/misc/switch-servers/  

Are you copying the Wordpress database as well?

You are trying to switch servers and upgrade at the same time.  I would strongly suggest you do that in multiple stages: first move to the new server using the same versions of Wordpress and CiviCRM - make sure that is working correctly, and then upgrade.

Switching to a new server involves changes with URL's, directories, passwords etc so get that set of issues resolved first.  That is often more tricky than upgrading.

You are also going from 4.4 to 4.7 which is a big leap. Opinions vary as to the best way of doing that: a single upgrade should work, but you may be better to upgrade to the last 4.5, take a backup, upgrade to the latest 4.6, take a backup then go to 4.7. It is extra steps but may save you time in the end if things go wrong.

To your issues with passwords: to dump the databases from the old server, you need the password for the old server.  When you load it to the new server, you need the new password.  civicrm.settings.php needs to have the new passwords but the changes you need to make depend on which option you follow in the guide for copying the codebase (Step 4).

If that looks too daunting there are plenty of people at https://civicrm.org/partners-contributors who would help.  (Yes, I'm one of them!)