Links dropped with image

Have you tried if the same thing happens trying to insert the same image with the same link on a WP page/post instead of a widget?
Could you post the HTML code that you can see in the HTML tab of the editor?

<p></p>
<p> </p>
[caption id="attachment_224" align="aligncenter" width="180"]<img class=” wp-image-224″ alt=”Travel from your yard to the world” src=”https://www.stgcfl.com/wp-content/uploads/2014/01/Yardi-pocket-patch-2-e1388633523149.jpg&#8221; width=”180″ height=”33″ /> Travel from your yard to the world[/caption]

My tinyMCE also does not work.

The code you posted does not contain any link. Are you sure you are inserting the link in the right way?
I tried to add a link to your code using the link button, and it works fine on my WP 3.8 test site. The HTML code with the link becomes:
[caption id="attachment_224" align="aligncenter" width="180"]<a href="https://www.google.com"><img class=" wp-image-224" alt="Travel from your yard to the world" src="https://www.stgcfl.com/wp-content/uploads/2014/01/Yardi-pocket-patch-2-e1388633523149.jpg" width="180" height="33" /></a> Travel from your yard to the world[/caption]

I copied your code and pasted into the widget and it worked. I think when I added the link I was not making sure the image was highlited.

Any ideas why the icons in tinyMCE advance does not populate in the pages and post?

Thanks for your patience. I am a travel agent by profession and travel extensively, so I am always curious what part of the world the person I am talking to is from. Just being nosey. You don’t have to answer if you don’t want to.

For TinyMCE Advanced issues I’d suggest to post to their support forum.
P.S. I am from Italy.

I was in Rome last year. Have not been to Venice and hope to make it in the coming year. Love your country and people. My grand children are half Italian. I am Chinese. What a mix. Buongiorno and grazie.