I just installed HID lamps in my 2005 Silverado. One set for the low beam and one set for the high beam. They are very bright and cansee 3 times bettter . The only problem is that they come on as soon as I turn the key on and I do not have daytime running light . There is a set of driving lights below but not yet HID, all 4 of theses systems has its own lamp but only high / Low are HID

SOURCE: Auto lighting of daytime running (low beam) lamps

Yes. These are called DRL's or daytime running lights. It is law that vehicles manufactured after 1985 must have low amperage lighting on while running.

SOURCE: 2000 Cavalier driving lights no-op

ok you said you have replace the bulbs, i believe you. your problem is still the bulbs, use type HS 905, both bulbs must be the same make and model, or else one will have the same problem your having. one of the two headlamp bulbs has blown, thats why the daytime running lamp is flashing.

SOURCE: i have a 2003 chevy cavalier. headlight issue

The blinking light is telling you that you have a headlight out, if you look the service light should be coming on when the light stops blinking.
Replace the head light and all should be fine.

SOURCE: low beam headlights do not work

replace the bulbs

SOURCE: bright lights won't work

I too had the same exact problem on my 1999 Cavalier. I replaced the lamps,then the DLR,and then looked at the harness under the battery box.(It appeared to look ok and didn't have any corrosion on it I could see). I then ordered a new turn signal/high beam switch that's on the steering column. I replaced the switch and still had the same problem. Not wanting to let this defeat me I started tracing the wires from the high beam lamps back. When I got back to the wiring harness under the battery box I noticed that just one of the wires had a little corossion on it. Guess what? it turned out that was the high beam wire and it was coroded through and not making the circuit complete. I cut the wire at the coroded spot, restripped both ends and twisted them together. At that point I tried all the lights and they worked perfectly. I then soldered and shrink wraped the repaired wire. (Finally end of problem) My suggestion,Really look closely at that wiring harness. If you have to use a magnifiying glass do so. This was a really frustrating problem that I finally solved and I hope this can help others with the same problem.