I have set z-index:200 for every single component of the menu (just to prove my case) and still it goes under the button. The button has a z-index:1 (<div id:bannerTeaser>).
Your #navbar isn’t positioned and therefore z-index won’t take effect as it only applies to positioned elements. You would need to add position:relative for it to be applied.
However it still won’t help you because navbar is contained within #header which has position relative set and ie6 and 7 mistakenly apply a z-index of zero to positioned elements when they should in fact be auto.
So as far as IE6 an 7 are concerned you need to address the positioned parents z-index before the stacking level of its children will be affected.