Guess what, I found the problem and a temporary solution. There is a bug that has to do with how the Program handles "Transparency". Now the only question is does this problem affect all Operating Systems, or just Windows Vista.
While any OS can use "Transparency" with the help of Third party Programs for Windows (Yes, I know Linux does Transparency), Vista uses it built-in for their "Aero Display". Anyway this should now be a easy Fix for them now that we all know what the problem is.
Solution: Turn off Transparency for now if you want to use the Shared Analysis feature

Now for more Bad news. While this fix seems to work fine on my Core2Duo Laptop or systems with 2 CPUs, on my Core2Quad or systems with 4 CPUs the Rybka.exe crashes when trying to load the 2nd (B) engine. But hey I am now halfway there, at least I now get the second window.

Hope this helps some of you.
System Specs
Core2Duo (Laptop)
Windows Vista 64-bit
Intel Video Card
T5450 @ 1.66 GHz
4 GB Ram
Core2Quad (Desktop)
Windows Vista 64-bit
Nvidia Video Card
Q6700 @ 2.66 GHz
8 GB Ram