Check the ITS Service Notices page for any service outages in the Taleo system:
On the Human Resources Current Vacancies page, make sure you're logging into the internal version (for staff) and are using your University username and password.
The other login section is for people not employed at the University who have set up a username and password to access the profile they use when applying for vacancies (public login).
If you receive an email from the site asking you to follow a link to reset your password it means you were trying to log in via the public login not the staff one.