This means that you want to set a new password for the database user root to new-password on the host localhost. I would guess that if you already set a password then you will need to include the -p flag so that it will prompt for you to enter a password (the one you already assigned). That is what I get from the access denied error.
The failure to connect to server part makes me believe that your mysqld is not running. Try starting the database first. Also try 'man mysqladmin' you can also check out the documentation on the mysql
website, it is fairly comprehensive.