I don't get why the permissions fix did not work. So when you boot from a cold start now, what happens exactly?
To get a clean start and restore from Time Machine will fix it, but you want to pick a Time Machine restore point from before you did this for it to work... otherwise you will "restore" the error right back.
Do this. Plug in the TM external and option key boot, then select the TM disk to boot from. Start Disk Util and erase Macintosh HD. Quit Disk Util. Now click restore and you will get a screen with a list of dates representing backups sets. Pick the one you know is before you made this mistake and tell it to restore.
That should get your machine back exactly like it was.