In IIS Manager, go to the website and in the IIS section, select the Authentication icon and open it. You should have a list of authentications. Right-click on Anonymous Authentication and select Edit. I believe that this should be set to Application pool identity. If not, then select this.
Next, go to the Application Pools and select the pool your website is in. In the listing, you should see the Identity column. It should be NetworkService for the pool in this column. If not, then right-click on the pool and select Advanced Settings. Under the Process Model section, set the Identity to NetworkService by clicking the button on the right-side of the text box and in the dialog, using the Built-in account dropdownlist.
Try your website now through IIS.