2002 Mitsubishi Galant cruise control will not operate when headlights are on
Are your headlights and cruise control both on the same lever on your steering column?
If so, you most likely need a new multifunction switch.
You could try spraying the switch with electronics cleaner, work the switch, and spray again.
I would start by cleaning the battery to chassis ground connections. A bad chassis ground connection could cause an excessive voltage drop to occur due to high current needed by the lights. If turning on the blower to high causes the same trouble then a bad ground connection is really suspect.
Check and see if one of the rear license plate lights is burned out.
Also check if your tail lights, brake lights and rear turn signals are working properly. An incorrect bulb can cause the brake lights to be on when the headlights are turned on. The cruise control will not function if the brake lights are on.