Brian, Alex, You're my savior! Now I finally got out of this hell. I really appreciate your help from my bottom my hearts. There were so many variables which would cause this problem. Without your help I would not be able to solve this problem within a day.
I finally realized that a resident Firewall program is installed on my note book PC by my company's IT person. It was this program that blocked X protocol packets between PCs outside of the company network ( this is why it was working when I was on my company's VPN network ). I was paying too much attention to other things such as Firewall configuration on my router. I disabled all Firewall options on my router and thought I was done with it, which was awfully wrong. If it were not for you I would not be able to think about Firewall again and would have killed few more days... I learned great tricks from you. I hope other people would get benefit out of this thread as well. Thank you very much :-)