The first thing you should check, is the SQL Server service up and running. If it is, check your connection string, especially have a close look in the instance name. For examples, have a look at
SQL Server connection strings - ConnectionStrings.com[
^]. These should help you to connect to the instance
What comes to listing the instances in the drop down list, make sure that SQL Browser service is running. For detailed information about this service, look at
SQL Server Browser Service[
^]