'99 Cavalier Hi beam problem

I have a '99 Cavalier where the hi-beams aren't working at all. My husband checked the bulbs and the switch and both seem to be ok. When I try to turn on the hi-beams, my Daytime Running Lights come on instead. We have checked all the fuses and the connector at the switch and nothing comes up. Any ideas what the problem could be?

I am having the same problem in my 98 Z24! Also, my daytime running lights WILL NOT turn off! I shut the car off and they still stay on. Any advice from anyone?