I have the same problem. When the Custom sidebars (v1.1) plugin is installed the TinyMCE WYSIWYG editor is not displayed within the Black Studio TinyMCE Widget and the html tab is greyed out. A text area is present and when content is added to this it can be saved albeit unformatted.
I have deactivated all plugins except Black Studio TinyMCE Widget, Contact Form 7, Custom sidebars, WP Display Header, WP Super Cache.
Using Responsive theme Version 18.104.22.168 and WordPress 3.5.1.
Now here is what is really strange! a second website that is not hosted at the root, http://www.rowantreetravel.com works fine with the same configuration, except that it was the second web site I build, so the plugin installation was more straight forward.
http://www.joyceraybooks.com does not work and it is the at the root of my hosting account. It also does not have drag and drop from the widget list working (rowantree does have drag & drop of TinyMCE Widget to the sidebar widgets). I have to add widget to specific widget areas instead of drag and drop. This may be the source of the problem but I cannot find that problem either.