First connect to the mysql command line and update your client password with the old_password() function like this:
mysql> UPDATE mysql.user SET Password = OLD_PASSWORD('newpassword') WHERE Host = 'hostname' AND User = 'username';
mysql> FLUSH PRIVILEGES;
note that if the database is running on the same machine as the php script, then you might replace 'hostname' with 'localhost'
The mysql docs do suggest one or two other approaches to solving this problem (http://dev.mysql.com/doc/refman/5.0/en/old-client.html) but this one is by far the simplest
christo