Can’t Remove Widget

I can’t seem to remove the Blogroll/Links widget from my template/theme at http://www.capsblueline.com

I researched it a bit and while I did not ever add all widgets I have tried (without success obviously) dragging the Widget to the far left corner and far right side of the ‘Available Widgets’ box. The ‘Links’ display doesn’t change size or shape, and although the display returns to the ‘Available Widgets’ box and it appears from the admin screen that the problem should be fixed, the Links box is still on display on the blog