telnet <your.mysql.server> 3306. If no
connection can be established, then either your server is behind a firewall
(the simplest remedy would be adding some
like here), or it's not listening on the standard MySQL port
(in this case you have to edit
my.cnf to enable networking, like this, for instance).
Then, if it didn't help, make sure your MySQL user is allowed to connect
from your specific IP (the IP of your Minecraft server in this case):
firstname.lastname@example.org must exist and have privileges
that you need.
Finally, phpMyAdmin is a Web-based software, and the IP of the user you
are trying to use to access your MySQL DB is should be IP of the server
where phpMyAdmin is installed, e.g. if phpMyAdmin is installed on the same
server as MySQL, then it uses
user_name@localhost in order to
connect to your database.