>>>>Are you connecting on the same box where you have the SQL Server installed? If not, have you tried connecting by specifying the name manually?
>>>>
>>>>Usually DBA don't activate the SQL Server Browser service. You should know the name of the server to connect.
>>>
>>>According to the IT customer guy (who is not a DBA; they don't have a DBA) the SQL is installed on the same box where I am connecting. He also cannot see the name of the server when going to SSMS. But when I go to the Programs -> SQL -> Configurations Manager I see that SQL Server is running. So I presume that I am connected to the right box. There are two things not running on in the Configuration Manager:
>>>SQL Server Browser and SQL Server Agent.
>>
>>If you open SSMS on this computer, are you able to connect using (local) as Server name?
>
>Yes. This is helpful. At least I can connect this way. I will just have to figure out the server name to put in the connection string of my application. Thank you.

Just try

select @@SERVERNAME

to get the server name.