To access your business page, you must be logged in to your personal profile. You do not need a separate password to post to your business page, just administrative access. If you do not have administrative access, "like" the page and e-mail firstname.lastname@example.org with the e-mail address associated with your personal account.
If you do not have the password to your personal profile, click "forgot password" underneath the box to enter your password on the Facebook home screen. Then follow the instructions from Facebook.