Login failed for user 'DOMAIN\MACHINENAME$'

I know this is almost a duplicate of : The error "Login failed for user 'NT AUTHORITY\IUSR'" in ASP.NET and SQL Server 2008 and Login failed for user 'username' - System.Data.SqlClient.SqlException with LINQ in external project / class library but some things don't add up compared to other appliations on my server and I am not sure why.

Boxes being used:

Web Box
SQL Box
SQL Test Box

My Application:

I have an ASP.NET Web Application, which references a class library that uses LINQ-to-SQL. Connection string set up properly in the class library. As per Login failed for user 'username' - System.Data.SqlClient.SqlException with LINQ in external project / class library I also added this connection string to the Web Application.

The connection string uses SQL credentials as so (in both web app and class library):

 <add name="Namespace.My.MySettings.ConnectionStringProduction"
        connectionString="Data Source=(SQL Test Box);Initial Catalog=(db name);Persist Security Info=True;User ID=ID;Password=Password"
        providerName="System.Data.SqlClient" />

This connection confirmed as working via adding it to Server Explorer. This is the connection string my .dbml file is using.

The problem:

I get the following error:

System.Data.SqlClient.SqlException: Login failed for user 'DOMAIN\MACHINENAME$'.

Now referencing this .net sql-server sql-server-2005 web-applications iis-6