Use Captcha (only) as password to access hidden content across entire site

I am looking for something or a suggestion as to how to have a vistior enter a captcha (and nothing more – ie no username / password) that would allow them to see otherwise hidden content on the site.

Hidden content might be a widget area, a page, post … or content within any of these.

I also want it so that if they solve a captcha on any page – ALL areas of the site that would have been hidden are now accessible … and preferably remembers the computer so they don’t have to enter a captcha each visit.

Any direction, insight, suggestions would be gratefully received.

Thanks,
Simon