MySQL error: 'Access denied for user' or 'failed to connect'

MySQL error: ‘Access denied for user’ or ‘failed to connect’
PROBLEM: You are running MySQL 4.1.x. As of MySQL 4.1.X there is a new password hashing system. PHP4 does not have builtin support for it as of yet, however PHP5 does. In order for your old PHP4 MySQL clients to be able to connect to the MySQL 4.1.X database you need to set an OLD_PASSWORD. You should be able to run the following Query to make it possible for PHP4 to access the MySQL 4.1.X database.
SET PASSWORD FOR ‘username’@’localhost’ = OLD_PASSWORD(‘password’);