The lights in one quadrant of the house (front porch, entryway, half of basement directly beneath entryway, hall closet next to garage, and half of garage closest to the entryway) do not work. The outlets in these spaces do work. None of the breakers were tripped upon opening the circuit breaker box. We flipped every circuit breaker on the circuit breaker panel off then on. This did not resolve the problem. Can anyone help with this?

Sounds like you have a broken wire or failed electrical junction somewhere. Could be hot or neutral. May require some hunting to locate.

And it could be a failed breaker. If your circuits aren't mark you will need to test them all. Test across the black and white from each breaker to insure you have power goping out down the line. If you do then I am with KC13, check each fixtire for a loose of broken connection. If wire nuts were used undo each, twist wires with linesman plyers and reinstall the wire nut.