Facing 'unable to access account name or password' error on MacBook

I am trying to access my computer's system settings. I get the message "unable to access account name or password." Clicking "OK" does nothing - the message remains. I looked at some previous questions and I am having no trouble with receiving email. The message has been on my computer for quite some time but wasn't affecting anything I was aware of until now. Right now I am simply wanting to adjust the setting for the screen saver as it doesn't seem to be working. My Apple account works as I have purchased music recently. Advice/help is appreciated.

[Re-Titled by Moderator]