I receive the following error when trying to connect users to our new SQL SDE Geodatabase in ArcGIS 10.2.2. Unable to connect to database server to retrieve database list, please verify your server name, user name, and password info and try again. Failure to access DBMS server. The SQL ports are open between the field office servers and the SQL server. Any assistance with this issue will be greatly appreciated.
Are you able to connect using SQL Server management Studio? If that is not working, ArcGIS won't be able to connect as well.
I'll sugegst installing just the "SQL Server Management Studio" on the field office server and try connecting to the database instance. See if that works.