I think we might have a mismatch on terminology.
cannot determine if I am using the latest form of WordPress
All sites on WordPress.com are running a highly adapted version of the standalone WordPress software. We don't have "versions" and what we have is always the most up-to-date and then some. You might want to read this for background http://support.wordpress.com/com-vs-org/
A Photo Carousel is a full screen layover that displays your Gallery photos. This can be used in conjunction with the tiled mosaic and default thumbnail types of Gallery.
A Slideshow is embedded in a post or page that also displays your Gallery photos. You can't use the Photo Carousel in conjunction with the Slideshow.
If you want to display only a single photo in your sidebar that leads to a specific post with a Gallery or Slideshow, you can use the Image Widget in your sidebar to do so. http://en.support.wordpress.com/widgets/image-widget/
When configuring the widget, for the "Link URL" simply use the URL of the post or page where you want your visitor to be taken.