After the levees broke, the second crucial thing that happened was Knucklehead Nagin declared New Orleans open season for looters. It appears that that then led to the break down in public order which was the key problem that New Orleans suffered between Tuesday and Friday when the National Guard started to arrive.
Let me know if I am mistaken in my assumptions on where the real problems occurred?
Yes.
Yes, there was a delay but being in a Storm Surge area, surrounded by lakes, is precisely why the levies failed. Whatever level the lakes were at, the storm surge "topped them off".
It has been predicted for years that the levies would not survive a Category four.