Ensure CB Core is public and published in CB > Plugin Management (you shouldn't be able to unpublish it, but access isn't restricted at this time). If it already is ensure the core tab Contact Info in CB > Tab Management is published as it by default has all your core fields on it. If it is check within CB > Field Management that you didn't disable registration output of your core fields (e.g. username, name, email, etc..). All of this should default work out of the box and should never be blank unless deliberately configured to be blank or a 3rd party extension is breaking the component output.

Turn on Joomla debug to maximum level and see if the blank page gives more info.

Typically you shouldn't be changing a plugins access permissions to begin with unless you absolutely understand the purpose of doing so. Reset them all back to Public is my recommendation. You typically control access to the content of those plugins by other means (e.g. their tabs if they have any, Joomla menu items to them, their content that they display directly has access parameters, etc...).