The error is due to the MySQL OLD PASSWORD method not being supported. You will want to update the MySQL password (not the PHP Live! database password) using the standard PASSWORD method.
1. Access your MySQL database
2. Select the "user" table. For each user update the password and select the PASSWORD from the Password dropdown menu in the password column. Or, for command line method, it would be:
UPDATE user SET password = PASSWORD('your_password')WHERE User = 'the_login'
3. Save settings, reload privileges (or restart MySQL server)