You will need to start browser service to resolve non-default instances. Additionally, opening UDP 1434 will allow resolution of the named instances by name instead of port, so you will not need to use the ports. If you are uncomfortable opening UDP 1434 long-term, or you have a DBA who is on-site and can connect locally, you may ask them to connect via SQL Server Mgmt Studio OR SQLCMD and specifiy the server connection as follows:
tcp:servername\instancename
prefixing with tcp will force a tcp connection. Once this is done, you may connect to your named instance and query sys.dm_exec_connections to find the port the non-default instance is running on like so:
SELECT local_tcp_port FROM sys.dm_exec_connections WHERE session_id = @@SPID
If you're on a named instance, this is not always the case though – Mark Henderson – 2009-08-29T23:08:23.927
For a named instance the port number is dynamic by default. – mrdenny – 2009-08-30T02:00:08.753