Host 2 sites on one server with 2 IPs

I have two domain names www.site1.com and www.site2.com. I have one dedicated server with Windows Server 2008R2 on it. Because the first site has SSL it uses an IP for itself, so I purchased a second IP for the second site.
The first IP is used also for nameserver.
I set up the first site over a year ago and it works perfectly. Now I want to add the second site with its IP. I have done the following:
I added the site on IIS and edited bindings on for the second site, as following:
site2.com                  123.123.123.123   80
www.site2.com        123.123.123.123   80
123.123.123.123      123.123.123.123   80
I also added the second IP on advanced IP settings of the servers network card.
On the ISP of the second domain name I 've added the same nameserver as for the first name (actually the 1st IP Address).

Now the problem is that although the first site works fine even if I call it with the domain name or its IP, the second site works only if I call it with its IP. It doesn't work when I call www.site2.com.

Help, help, help!!!!