If you can access PHPMyAdmin, assuming you are using the standard MySQLdatabase, it will find the database for you, so what you can do is to run a backup of the database and then using PHPMyAdmin again, restore it to the new server. It is named whatever the name was given at installation, but "moodle" is default.
Otherwise, the location of the database is wherever it was put when your Moodle was installed. You might want to ask your sys admin people, they may not have used a default location, but often it is the MySQL folder on the active drive.
The database and the moodledata folder are separate things. The moodledata folder is on the same drive as the Moodle, but usually one level above the Moodle in the directory tree, for security purposes. You can confirm that by looking at the tree of your server, again, your installation may be different.