The problem is simple: If I set the webserver's IP address as my desktop's default gateway in TCP/IP settings, I cannot open any locally hosted site at our webserver on my PC. I can open any other site from the internet as well. If I use a real IP address then I can open our sites too.
The previous webserver was Windows Server 2003 Webserver Edition, and it had no problem like this. The newer one is Windows Server 2008 R2 Standart Edition.
All clues are now listed. If you need any info or got idea, I'll supply more on request.
Addition & correction a bit:
I cannot open any site if my IP is local. ie: webserver 192.168.35.211 mydesktop 192.168.35.45
- I can telnet mysite.com 80 but there are no responses to my requests.
- I can telnet mysite.com 25 and there is response.
- VPN connection from home to Webserver makes the sites "offline" to me. I can still open supersuser.com thru Webserver
So I think there is IIS related problem instead of network.