Time Machine worked fine w. new HD for 16 backups, but started giving this mssg: [TIME MACHINE COULDN'T COMPLETE THE BACKUP TO "TOSHIBA EXT" ...An error occurred while creating the backup folder]

Make sure your hard drive is formatted properly for the operating system installed. Go to Apple menu -> About This Mac to determine what it is. You posted to the 10.5 forum, but your signature says you have 10.9. Here is the tip on what formatting supports what operating systems:

https://discussions.apple.com/docs/DOC-3003

just turn off your MAC...zap the PRAM twice on restart and it should work fine.....that worked for me as I had the exact same issue...