"Login failed for user 'domain\machinename$'.
If the login is originating from a service on the same server as the SQL Server you can see this error message when the actual login is from a virtual account. For instance if a local SSAS instance is connecting with the default service account, you need to grant access to
NT Service\MSSQLServerOLAPService
even though the login failure displays the machine account. These virtual service accounts will use the machine account when connecting to remote servers, but not for local resources.