2003 Dodge Neon lights

Not only check fuses, check that the fuse circuits go hot, when they should. The problem may lead back to the multifunction switch, if that switch is in the steering column, and there is an airbag in the steering wheel, then there is a safety issue.

You might wiggle the wires at the headlamp see if it makes any difference. You could check for voltage and ground at the headlite. Some headlite bulbs, you shouldn't touch with your bare fingers.