Before proceed we need to know while restoring data in noarchivelog mode that,

1)Only cold backups (that is, backups created when the database was shut down normally) can be used in restoring a database in NOARCHIVELOG mode.

2)Media recovery is not possible, because there are no archived logs.

3)If we exclude any tablespace except read-only or offline from taking database backup then those tablespaces will be lost.

In this scenario I have lost all the data files, control files, redo log file and spfile. I have also forgot DBID of the database. The procedure of restore and recovery of database in noarchivelog mode in as below.

A) Find the DBID of the Database from Backup Piece.

bash-3.00$ strings /oradata2/flash_recovery_area/DBASE1/backupset/2008_05_06/o1_mf_nnndf_TAG20080506T111057_420x821v_.bkp |grep MAXVALUE,

3386862614, MAXVALUE,

We got DBID here 3386862614.

B) Connect to target database with RMAN

bash-3.00$ rman target /

C) Set the DBID.

RMAN> set dbid 3386862614

D) Start the database in nomount stage with dummy Parameter.

RMAN> startup force nomount
startup failed: ORA-01078: failure in processing system parameters
LRM-00109: could not open parameter file '/oracle/app/oracle/product/10.2.0/db_1/dbs/initdbase1.ora'

starting Oracle instance without parameter file for retrival of spfile

Oracle instance started

E) Restore spfile

RMAN> restore spfile from '/oradata2/flash_recovery_area/DBASE1/autobackup/2008_05_06/o1_mf_s_653998009_420shstm_.bkp';

F) Mount the Database.

RMAN> startup force nomount;

G) Restore controlfile.
 
RMAN> restore controlfile from autobackup;

RMAN> alter database mount;

I) Restore Database. 

J) Recover Database: 

RMAN> recover database; 

RMAN> alter database open resetlogs;
 
database opened.