Firstly, if the Web Proxy is to show anything in current sessions or log any activity, the client browsers must be set to use the Proxy server.
I have experienced the client browsers displaying nothing once configured to use a proxy server beforeand I found that disabling anonymous access to the default web fixed it.
Disabling anonymous access simply ensures that users be authenticated to access the Default Web Ste and, by association, the Proxy Server. It should not restrict use of theProxy Server as, presumably, your clients are already logged on to the domain. It improves client?s ability to access the Proxy Server when access control has been enabled on the Web Proxy?s permissions.
Another thing that occurs to me from your last comments is using IIS to keep a backup copy of your Web site locally; this is very common and should not cause any problem. My only query is how was this done?
The best way is to create a virtual directory in the Default Web Site and, if required, set the home directory of the Default Web Site to the location your backup is located.
I have known some sites create a new Web Site just for this purpose and then stop the Default Web Site. This will adversely affect the operation of mostIIS services and should be avoided at all costs. However, if your Outlook Web Access is operating correctly then I would guess that this is not the case here.