MySQL PHP incompatibility

The MySQL account you’re using probably has an old 16 character long password (hash).
You can test that with a MySQL client (like HeidiSQL, the MySQL console client or any other client) and an account that has access to the mysql.user table. If the Password field contains 16 chars it’s an old password and mysqlnd cannot use it to connect to the MySQL server.
You can set a new password for that user with

SET PASSWORD FOR 'username'@'hostmask' = PASSWORD('thepassword')

see dev_mysql_set_password

edit:
You should also check if the server is set to use/create old passwords by default.

edit2:
Please run the query

SELECT
  Length(`Password`),
  Substring(`Password`, 1, 1)
FROM
  `mysql`.`user`
WHERE
  `user`='username'

on the 5.0.22 server (the one that’s “failing”). Replace username by the account you’re using in mysql_connect().
What does that return?

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