Hi Peggy,
Now let's see... where to start...
It's always a good idea to use a standards compliant browser as your development browser, even if you wish to use IE as your regular browser.

Firefox is often the recommended one, since then I can recommend the Firebug plug-in and others that will make your development work much easier.
Using FF and FB you can easily identify what elements in the rendered page of your site are giving you problems, and can see what classes or ids to adjust in the stylesheet.
Yes, you will have to learn about CSS at least, though you can get by without any PHP knowledge. I do.

Google up some links with "CSS tutorial" or get a good basic book. Play around with it in an HTML test page first to get the feel of it, then start working on your Zen site. Pay particular attention to margins, paddings and widths -- they will be very useful in working on your Zen template.
Which reminds me, see the tutorials/FAQ link at the top of these pages and pay close attention to the Template Customization/Building Overrides section.
I had a look at your links and I can say with confidence that you can do what you want. But I see the image at the top is not the same. So start by cutting and stretching the image so it's the size you want. Then you'll be able to put it into your Zen site and 'shrink' the header around it. That will get you started. The rest will follow fairly easily, though not entirely painlessly.
By the way, I checked out your Totally Shameless link too and I've applied to join the forum. But I noticed that your links on the right side of the home page disappear when I hover over them. In other words, the hover style in your stylesheet is applying the same colour on hover as the background colour. That's your first CSS project! Get to it!
Rob