Depends on if your backup was done with the database up or down.

If the database was down, everything should come up OK.

If the database was up, you still have a chance to restore.

Either way, you can recover using a backup control file:
1. copy the restored control file to the locations your original control files were located.
2. start the database in mount mode
3. recover the database using the backup controlfile (alter database recover until cancel using backup controlfile).
4. keep applying archived redologs until just before the problem.
5. alter database open resetlogs.

(This procedure is outlined in note 69468.1 on metalink.oracle.com.)