The problem as you said is your navigaiton disapears on the left. This is because of your negative value for margin-left on the #leftnav ul. Im not sure why its doing that, im assuming IE7 simply doesnt like the margin-left you have used. So i cant really give you a way to fix it other than to used a margin on your list-items, rather than the list itself.
Instead i just modified your old css, it may need to be slightly changed for you arrow image, because i dont know how big it is so i couldnt do it for you. Hopefully this fix will suffice. Good luck with your project.
Css
Code:
#leftnav {
background:#63ce28;
font-size: 12px;
width: 190px;
float:left;
margin:0px;
padding:0px;
}
#leftnav ul {
margin:0px;
padding:5px;
}
#leftnav ul li {
list-style:none;
}
#leftnav ul li a {
height:22px;
line-height:22px;
margin:0px;
font-weight:bolder;
display:block;
color:#14637f;
text-decoration:none;
}
#sub_button li {
margin-left:10px;
background:url(images/arrow.png) 0 0 no-repeat;
text-indent:15px;
}