Only one dropdown menu opened, the one under solutions in both FF and IE. It was a huge dropdown though and hierarchical one, too.
Nice work! Seems that you have solved the problem, because your site opens the same way in FF and IE 6.0 from my computer. It's a very nice and professional looking site.
Your CSS looks looks like a total mess though You have both internal and external CSS and it just all over the place. Why don't you put everything into external CSS files? What server-side scripting language did you use?