Our setup is like this, we have a webserver that runs an asp.net website on it, this website makes web service calls to another IIS site over https, last night all webservice calls started failing. I went on to the box and tried to bring up the website in IE (tried both 7 and 8) both failed with the error message "Cannot display the webpage" I then tried Firefox on the system, and the remote HTTPS site loaded just fine. As far as I can tell IE and by extension Windows are failing on the SSL handshake (IE receives a TCP RST command after the handshake, verified this through Wireshark.)
I'm not really sure where else to look with this issue, but any insight would be greatly beneficial.