The contribution page displays just fine when the member is NOT logged in to my site. I have Joomla 3.6.0 and CiviCRM 4.6.19. However, when the member is logged in, the contribution page does not display and instead the link throws you back to the homepage. Since the page is open to the public, I can't see where this problem is coming from.
Have you checked the permissions in CiviCRM?
If, say, profiles are set to be viewable only by Guest and are included on that page, then it would only be viewable if not logged in.