I agree with the dimmer switch being the cause of your problem, but not because of a ground problem. The switches are not grounded to operate. They have one input from the light switch and one output each for the high and low beams. The only switch that is grounded to operate is the wiper switch. OK, and the dome light switch on the headlight switch!

The problem with your front parking lights must be a different problem. They are separate from the headlight circuit. All the running lights are on one circuit; parking lights, tail lights, side markers and license plate light. About the only way to troubleshoot this is to follow the brown wire between the light switch and the parking lights and see where there is a break. Of course, both bulbs might be out, but they would unlikely go out at the same time.