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.
What I would do if I where you, and I had some time on my hand, is to run Migration Assistant. From there you can restore your account with all your information from your latest backup.
However I should mention, the "full backup" thing—never heard of it, and I have used plenty of Time Machine restores, however the migration assistant approach is the best way to give your mac a fresh boost too, hence it doesn't load all the OS parts, only your home directory!