How to recover data from iPhone backup files WITHOUT the info.plist, status.plist, manifest.plist, manifest.mbdb, and manifest.mbdx files?

I have iTunes 10.5 and Mac OS X version 10.6.8.

I would like to restore my iPhone from backup.

iTunes detects all my backups EXCEPT one, which happens to be the backup I want. 

I looked in the backup directory (~/library/application support/mobilesync/backup) and IT IS THERE along with the other backups. HOWEVER, unlike the other backups, it's missing five files: info.plist, status.plist, manifest.plist, manifest.mbdb, and manifest.mbdx. 

I have tried applications that can extract data, like the free iPhone Backup Extractor for example, but they work only if I have the five files. 

Is there a way to recover data without the five files?