The dialog launcher is the little arrow button in the bottom-right corner of a "group" on a tab. Groups are designated by titles along the bottom of the tab.

In Word 2013 everything generally looks grayed-out to my eyes used to the color of Word 2010. In the image above from the Page Layout tab six of the buttons in the Arrange group on the far right are actually grayed out. Are you saying that your Margins button looks like one of these? If so, what happens if you click on the dialog launcher?

If these are grayed-out, and the dialog launcher does not work, this would indicate that some sort of document protection is in force. I would use the Developer Tab to investigate under the Restrict Editing pane.