PASSWORD() function no longer working after server move

I have moved my website and MySQL database to a new, free server at webhost.com, running MySQL 5.0.91-community.

Already, I have noticed that the MySQL server "does not like" the following query:

SELECT * FROM users_tb WHERE user_name='student' and user_pass=PASSWORD("password_here").

I 开发者_如何转开发have tried it in PhpMyAdmin, where no results are returned. If I leave out the password clause and just search by username, it works.

This code worked on the previous server. What has changed?

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PASSWORD behaves differently depending on (1) the version of MySQL, and (2) whether or not the admin has activated old-passwords in my.ini.