Why is it that I can no longer access some folders in my old time machine backups and how can I get access?
Have you tried repairing the disk permissions via Disk Utility? 

If that doesn't work, try enabling the root account, logging in, and attempting to access the files. 


  
  Use the "System Administrator" account to access the files:
  
  
  navigate to the folder "/System/Library/CoreServices/" and open "Directory Utility.app"
  Click the padlock
  in the "Edit" menu, choose "Enable root user"
  from the Apple menu, choose "Log out"
  log in as "System Administrator" (or "root") and you will have access to the files in "/Users/Abby"