It will likely be permissions on the SQL instance.
It's easiest to troubleshoot if the RDC is running on the SQL box. That way you can connect to 127.0.0.1 which SQL treats as a secure connection. Ensure that the SQL instance has a binding to port 127.0.0.1, TCP is running and SQL is a single instance. Also ensure that Mixed Mode Authentication is being used on the SQL Instance.
If you are not running a single instance of SQL then you will have to append the instance name to the 127.0.0.1. It's easiest if you play around with ODBC connections in Control Panel first to a) ensure that things are working and b) you know which connection strings work.
You may also have to change the user context of RDC if it is running under a service account. Ensure this user has sufficient privileges to access your Database i.e. run it under a "real" user account that can access SQL and your database(s).
This should you get you a working although insecure setup. So start implementing whatever security etc you are comfortable with then a step at a time.
If the RDC is located on a different machine you need to make sure that the SQL instance "Accepts Remote Connections".
Good luck,
Mark S.