There are a combination of things. A number of differences in the way IE renders CSS from other browsers can be side-stepped completely by simply developing for FF how you want it to look, and then check IE, instead of the other way around.
That said - here are a few things which will make your site look how you want in FF - and it should still look the same in IE (not tested though) so you'll achieve more consistant results between browsers:

change this whole rule:

div#header h1{height:80px;line-height:80px;margin:0;
padding-left:10px;background: #EEE;color: #79B30B}

to:

div#header img { display: block; }

as you are not using a h1 anyway and using display:block on the img in the header will get rid of unwanted whitespace beneath it and making it more like IE.
Then change this rule:

div#navcontainer ul
{
padding-left: 0;
margin-left: 0;
background-color: #625F73;
color: White;
float: left;
width: 100%;
font-family: arial, helvetica, sans-serif;
}

to this:

div#navcontainer ul
{
padding: 0;
margin: 0;
background-color: #625F73;
color: White;
float: left;
width: 100%;
font-family: arial, helvetica, sans-serif;
}

only differences there are the margin and padding values are now 0 for all sides. Not sure which part of your code is giving that ul element a top and bottom margin but this fixes it.

These fixes have not addressed your side menu (not as wide as in IE) or your missing orange strip near the bottom - but at least the top area should all butt up now.