What is the parent of your IE7 that requires “Invisible connections”? I am using IE7, same build as your, without “invisible” when the parent is explorer.exe (the normal case, I think). However, I have another iexplore.exe in which Firefox is the parent(!) and this requires that I allow invisible connections: this entry results from the Firefox context menu option “View this page in Internet Explorer”, sometimes useful for badly constructed web pages.
I disabled edexter, hosts file and avast and it still needs invisible to work. So that rules out any loopback reasons for it (if there could have been any?).
I have quite a few windows services disabled, I might see if enabling them fix it. I might send iexplore.exe to avast or someone to see if its infected or something. I know its likely to be me and not CPF.