ApplicationPoolIdentity IIS 7.5 to SQL Server 2008 R2 not working

I had the same issue as well. As per this page, the ApplicationPoolIdentity is supposed to access network resources as the machine account (DOMAIN\COMPUTERNAME$), but it was using NT AUTHORITY\ANONYMOUS LOGON to access SQL server instead.

I was able to use this hotfix to get ApplicationPoolIdentity working as the doc says it should. This hotfix doesn't specifically describe a solution for accessing network resources as NT AUTHORITY\ANONYMOUS LOGON, but it's related to the computer password changing.

This stackoverflow thread helped me find this solution:

Other useful tips for debugging ASP.NET identity and SQL identity

Since SQL integrated auth is related to the thread identity, it's useful to be able to view your user identity, thread identity (which changes depending on impersonation), and the SQL server login. This ASPX snippet displays all three:

<%@ Import Namespace="System.Security.Principal" %>

<div>ASP.NET Request User identity: <%= User.Identity.Name %></div>
<div>Current thread/process WindowsIdentity: <%= WindowsIdentity.GetCurrent(false).Name %></div>
<asp:SqlDataSource ID="CurrentUserData" runat="server" ConnectionString="<%$ ConnectionStrings:ConnID %>"
           SelectCommand="select SYSTEM_USER" />
<asp:DetailsView DataSourceID="CurrentUserData" runat="server" />

I had the exact same issue. I pulled my hair out for several hours and finally rebooted the machine. The issue went away! Note that restarting IIS via iisreset DID NOT solve the issue. It only went away when i restarted the server.