Server :: MySQL Root User - Administration And Permissions

I'm using an older redhat system (2.6.9-22.ELsmp) here which is running an older mysql (server version: 4.1.12). I don't think that's the source of the problems. I believe that have understood things rightly when I say that the mysql root user is unrelated to the linux root user ... in my case I believe the root user to be the unix user mysql. So when I connect to the server (local host from a local terminal) I use:
Code:
-bash-3.00$ mysql -u mysql -p
and enter a blank password

This gets me on, however I seem unable to do anything like create database or alter privilege. I wonder if its related to my finding no database called mysql?
-bash-3.00$ mysql -u mysql -p
Enter password:
Welcome to the MySQL monitor. Commands end with ; or g.
Your MySQL connection id is 11 to server version: 4.1.12

Type 'help;' or 'h' for help. Type 'c' to clear the buffer.
mysql> show databases;
+----------+
| Database |
+----------+
| test |
+----------+
1 row in set (0.00 sec)
Although I understand that show databases will not show things I have no priv to see. Does this mean my settings for the users are all screwed? How do I rectify this situation? Some other (perhaps) useful information.

Code:
[root ~]# cat /etc/my.cnf
[mysqld]
datadir=/var/lib/mysql
socket=/var/lib/mysql/mysql.sock
# Default to using old password format for compatibility with mysql 3.x
# clients (those using the mysqlclient10 compatibility package).
old_passwords=1
[mysql.server]
user=mysql
basedir=/var/lib
[mysqld_safe]
err-log=/var/log/mysqld.log
pid-file=/var/run/mysqld/mysqld.pid

So my BASEDIR seems to be nothing like is suggested in the documentation at [URL].