Sorry Vekia, I fixed that faster than I thought I would. However, you can see the problem on the home page. It turns out the problem was coming from three modules: (1) HomeSlider (2) Assurance and (3) Favorite Products. I was able to diagnose it simply by viewing source in Chrome and searching for "http:". The code around the links labeled what module was generating the links - very eloquent BTW. Then I disabled the latter two problematic modules in the interest of time.
As for the HomeSlider, I decided that an SSL warning on the home page is okay, as long as the check out pages showed a clean SSL message. So you can still see the SSL warning in Chrome. IE just gives up and doesn't show a lock of any kind. If you view source and search for "http:", you can still see where HomeSlider is calling to the linked images with unsecure links. I found in another post where you diagnosed the exact problem and helped someone else replace the one problematic line of code. Kudos.
I read in another post on this forum that the CustomerAssurance (sometimes seen as Customer Insurance) Bar is fixed fairly easily. The problem occurs when you have SSL and leave the default images. Another poster figured out that if you download the default images and then upload them where the configuration says "no image selected" the module will start calling to the images using https links. For the sake of time, I just disabled the module.
Many thanks. All the help you have given others moved me through this process well.