iTunes cannot connect to Apple ID Server
After some time, I came back to this and tried some other things and got my iTunes connecting again.

On my Windows side, I use GData for my security and it has firewall settings, min-max.  I always keep it on max for tight security, but I tried lowering it to one below max and that worked.  Oddly, when I disabled firewall altogether, that did not work for me.  Also, sometimes I have to lower setting to two below max to get iTunes to connect.  Very strange, but it works.  

What is really strange, is that I could not connect on my MAC side either, which is not running GData.

I got a work around and I'm fine with that.

I hope this helps someone else.