You cannot start or stop the Oracle Internet Directory or the database from Oracle Directory Manager, although you can connect to Directory servers that are already running.
To start the Directory server processes, you need to have the OID Monitor (oidmon) process running and then issue start-server and stop-server messages through the OID Control command line tool (oidctl).
For additional information, see the chapter on starting Oracle directory server instances in the Oracle Internet Directory Administrator's Guide.