C# – ‘Domain/MachineName$’ being used for authentication instead of ‘Domain/UserName’

For a site to use the application pool identity for classic ASP, you need to change the credentials used for Anonymous Authentication. By default, the site will be set to use a specific user, namely IUSR.

Select Authentication from the IIS area of your site, then select Anonymous Authentication followed by Edit. Change from Specific user to Application pool identity.

It's advisable to use Windows authentication (integrated security) over SQL authentication so that you don't have credentials in your config files so that if those files are compromised, you don't lose control of the credentials.

To give Network Service read permission on the EventLog/Security key (as suggested by Firenzi and royrules22) follow instructions from http://geekswithblogs.net/timh/archive/2005/10/05/56029.aspx

1. Open the Registry Editor:
   1. Select Start then Run
   2. Enter regedt32 or regedit

2. Navigate/expand to the following key:

   HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Eventlog\Security

3. Right click on this entry and select Permissions

4. Add the Network Service user

5. Give it Read permission

UPDATE: The steps above are ok on developer machines, where you do not use deployment process to install application.
However if you deploy your application to other machine(s), consider to register event log sources during installation as suggested in SailAvid's and Nicole Calinoiu's answers.

I am using PowerShell function (calling in Octopus Deploy.ps1)

function Create-EventSources() {
    $eventSources = @("MySource1","MySource2" )
    foreach ($source in $eventSources) {
            if ([System.Diagnostics.EventLog]::SourceExists($source) -eq $false) {
                [System.Diagnostics.EventLog]::CreateEventSource($source, "Application")
            }
    }
}