First, let me say I couldn't agree more that government offices, corporations large and small and millions of individuals still use IE8 and want to assure you that I drive my colleagues crazy advocating for more resolution of this issue. I'm glad to have your support in that effort.
We have made some progress as now the NavBar works in IE8. But the feature slider is a problem. However, as Simon pointed out, we do provide the Browser-Specific-CSS plugin that will help you set CSS for IE8. When your site detects that browser, it kicks in the IE8 styling and the site is largely visible. Some things just never worked in IE8, like text-shadow, which surprisingly doesn't even work in IE9.
The problem with the Slider appears to be a transparency, shadow and likely, image scaling.
So, let me address those in reverse order. Scaling is taking the image from one size to another dynamically. You're familiar with WP
allowing you to change an image size when adding one to a post. Well, IE8 and 9 don't recognize even those changes. Hundreds of people over the years have complained about that here and on WP
.org. When the slider tries to use Aspect Ratio, it doesn't work. So, one trick is to make sure your images are all the same size and fit within the space you want them, considering padding and margins.
For the shadow, using Firebug or Chrome inspection tools, along with Browser Specific CSS, you want to simply hide it with something like display:none; in your code.
The same thing with transparency, except you can always substitute a color for the transparency, though I don't know what effect that might have in that browser. If it doesn't work, just display:none; the element if need be.
If you google IE8 browser specific CSS, you're going to find tons of sites giving you many great hints.
Don't give up. There's work to be done, but this is do-able. Patience is key, and research.
I apologize for asking so much work of you, but with CSS3 and HTML5 post-dating IE8, there's very little else I can offer.