What browser are you using? IE will not take the pseudo-class for anything other than an anchor. I assume that they are anchor links.
I don't know what you want with these images, but until we get right with:
<div id='ID_DivTopMenu' class='Div_TopMenu'>
.Div_TopMenu {...}, a problem remains. I see & note the class="" similar in name to this id, but there is no #ID_DivTopMenu in the CSS that I can see.
I don't know what more can be done for you. The HTML cites a DIV named id="ID_DivTopMenu", -I don't think that there is anything in the CSS called "#ID_DivTopMenu" and maybe that is part of the problem.. 
No live-hosting eh? Can you copy the ENTIRE code and past it into a post? The two segements that you showed aren't enough: -I re-built using them and see something entirely different than what your screenshot images show. Either we are using different browsers or user-agents (VERY likely.. -are you using Dreamweaver for this?), or, -there is some essential code not included (javascript probably, if this is a drop-down and we'd NEED that to see/test what you are doing and the code is quite ineffective without this)... :p
What I see, is a 20-or-30px tall navigation bar, about 50px wide, that is chopped-off at the bottom, and nothing works at all.. :o