You need to use oradim to create the service for the new database. You should have the pfile stored as %ORACLE_HOME%\database\initsidname.ora. This file can just be a copy of the pfile on the current server. Because there won't be any control files the database will startup nomount. You can specify the password for the new database when you create the service. connect to that service and you can restore the control files, then mount the database. At this point the control files will know where the backups are and where the data files should be. This is all basic RMAN backup/recovery stuff. You may want to read up on RMAN backup/recovery in tahiti.oracle.com.
$ is a unix variable, you need % for windows