I have a user with a laptop running Windows 7 Pro (64bit) and Office 2010 pro.
On the office LAN the Laptop runs Outllok 2010 ok, connecting to a SBS 2008, the client has the private security certificate loaded and OWA can be used without any warning message.
Outlook anywhere appears to be setup correctly and I have created the same account details on another laptop and tested the RPC/HTTPS connection, which worked fine.
No malware has been detected by either Symantec or malwarebytes. The user doesn't want the machine wiped and rebuilt.
I have attached a connection status screen print.