2002 Civic Headlights not working correctly

It could be driving lights mode instead of low beam. Check connections.

Try changing the headlights....some headlight high beams will work even when the low beams dont

High beams dont go on at all? Does the DRL light dissapear when u turn on the headlights? Now, because your high beams dont work, it more likely means that you need to replace your bulbs. Because if it would be a problem in the car itself, only the DRL system would fail. Im 80% sure that changing your bulbs will solve the problem.

If it's not the bulbs, be sure to check them, might be dual filament and the high beam wire is fine but the headlight one is shot, one bad wire would cause both headlights not to work.
Hopefully that's the problem, if not, it could be blown fuse/short in the wire. Try checking power/ground at the bulb to reduce the possible problems. If it has both with the headlights "on" then it's the bulb, if it's missing one then follow the wire for any irregularities.
They sometimes pass the wires under the flooring right near the drivers feet, which is a perfect place for water/salt to seep in and corrode wires.

Sounds like you need a bulb,the daytime running lights send power to the high beam wire so they look like low beam lights are on but really they are high beam lights running on low voltage.

if im understanding you correctly you have high beam lights but no low beam if this is the case it sounds to me like the switch is bad (the switch that controls the lights)

Might want to check the fuses if you haven't already.

it sounds like the actual lever is bad. looks like it is time to get it replaced

the comination switch

Look in the owners manual. There are four different fuses for the headlights; including one for each low beam and one for each high beam.