I had this same problem when I installed SQL Server 2008 R2 developer on a machine that already had an earlier instance of SQL Server Express installed for a specific application.
I was able to work around this by using SQL Server Configuration Manager to give each of the instances of SQL Server (other than the dedicated one for the specific application) a specific TCP/IP port (in Configuration Manager, look for Network Configuration, Protocols for the specific instance, and double-click on TCP/IP under protocol name - be sure to both enable the TCP/IP and select a non-used port, like 14330 or 14331)
Then, once I had assigned each instance its own TCP/IP port, use SQL Server Management Studio to connect to, e.g., .\MSSQLSERVER,14330 (be sure to use a COMMA, not a COLON, to separate the instance name and the port!), and you should be able to connect.
I did not need the SQL Server Browser service, probably because I was setting my own port numbers. In fact, SQL Server Browser did not help at all.