there is a number of things that could cause this. here are a few easy ones to check. is the e-brake fully disengaged. are the bulbs burnt out. is the wiring harness plugged into the daytime lights bulbs and in good condition. if these check out, you may have a fault in the daytime running light module.
there should be a fuse under the hood or under your fuse block that probably blew
the daytime running lites go out when you put the trans in park. they also go out when you depress the parking brake. i would start looking there.
Some makes of cars have their lights on all the time, usually if the manufacturer is Swedish, where daytime-running-lights (or DRL) are mandated by law. If you check the cars which have lights on during the day, you'll notice they'll be Volvo, Saab or some other Nordic manufacturer.
i think, depending on the year, that problem is caused by a factory defect.
If by "dim headlights" you mean low-beams... the bulbs are bad and must be replaced.
The Grand Prix models come with daytime running lights so they are on during the day, but the regular lights are controlled by a sensor and are set to come on in dusk conditions automatically and off when daylight is sufficient.
Bulbs burned out?
All of these parts run on electricity, and for all of them to fail would be bad. Bad or burnt wiring could cause them not to work, or a alternator going bad could cause them not to work as well.
You must have a cross wire or a loose wire somewhere you should check a good electrian.
Im Assuming you Should Check The Whole Lighting System. Usually it NOT the switch but could be. suprised me once when it was, but again usually not. The Daytime lights a separate from the Regular beams, check the high and low beams next before anything else. maybe just an old light that decided to Crap out?
your car sucks!
Mostly likely: blown fuse or bad bulb