Lost low and high beams on 2001 silverado

Fisrt of all you must determine if you are getting power to headlight switch. You'll need to pull to the dash panel out to get to the switch. Be careful to disable your air bags when working around the dash.With a test l;ight probe your connector on the back of the switch. You should have one battery powered wire . You probably do since you said your running lights work. Turn on your running lights only at fisrt. Probr the plug again. You should have power out on one terminal only. Then try your headlights, if you have power on the other terminals that didn't work with only running light, your switch should be fine. I'm betting that your problem is in your dimmer switch. I have repaired this problem many many times because of bad dimmers. Under the dash you will need to remove the plastic cover(typically held on with 7mm screws and push pin type connetors.). On the left side of your steering column there will be a switch with a single connector that has several wires in it. Look at the end closest to the steering wheel. You should see a rod about 3/16 diameter contacting one end of the switch.That's your dimmer switch.Carefully place a piece of masking tape on the rod to hold it in place. Unplug wire onnnector and then remove the two screws that hold it to the column.Look to see if there is any burnt wires/connectors there. If not probe the switch with your test light. Remember one power in and should have one power out on each beam. (possibly two on high beam for indicator) If no power out on any position of dimmer, it's bad replace it. If you do the problem is between the dimmer and he headlights.I doubt this is the case. When replacing your switch, make sure that you test the physical function of the switch before you install the cover etc.There is some room for adjustment where the screws mount it to the column. I've done this dozens of times and hope this helps you.