@Mike,
When configuring a ColdFusion SQL Server data source, if you don't specify a username and password, ColdFusion will attempt to authenticate to the database using the credentials of the account the ColdFusion service is running under. By default, the ColdFusion service will run under the "Local System" account, which will be unable to login to a SQL Server database on a remote server. You should configure the ColdFusion service to run under a Domain account specifically for ColdFusion, and make sure that same Domain account has been granted the correct permissions within SQL Server. Alternatively, if your SQL Server instance has "Mixed Mode" security enabled, you can create a SQL Server account for ColdFusion to use that has access to the necessary databases, and configure your ColdFusion datasource to use that login name and password.
For more details on configuring ColdFusion to run under specific accounts, you might take a look at the approriate lockdown guide for the version of ColdFusion you are running.
-Carl V.