Restored from Time Machine but NO applications
This question was also posted at https://discussions.apple.com/message/22138652. Based on the replies, it seems like /Applications/ was actually missing from the iMac and the snapshots.

I'd also recommend doing an upgrade install from the recovery partition. It should replace applications and other system files with the default versions but not affect most user files or settings.

A similar question where the OP had excluded /Applications/ from backups:


Full restore from backup, /Applications not backed up