Time machine full restore only shows "complete backups"
It appears that you disabled backing up system files by dragging /System directory to ignore list. "Full backup" means that OS X files are also backed up. It seems that in your case they are not, so you cannot restore the system from this backup.

Your way to go now is:


Backup the last time if you still can
Boot to Internet recovery if your Mac has it (if not, update EFI to get Internet recovery) or from disks that came with your Mac (if you have them)
Reformat the disk, keep "Macintosh HD" name
Install a fresh copy of OS using Internet recovery or disks
Internet Recovery will give you the same version of OS X as your Mac originally had. If it is not Mavericks, get Mavericks from the AppStore, make a bootable drive (google for it, it is easy), boot the drive, reformat the disk again and install fresh Mavericks.
On the last step of the installation you will be asked to migrate your files. Do that.


This way you will get a fresh copy of the system with all your files from the last backup.