Most likely a fuse or a bad ground.
Fuse, wiring, bulbs
Check the fuse for the headlights. It is probably open.
Fuse for parking lights probably blown.
Check the fuses and the bulbs.
in dash lights
if you've tried hitting the high/low beam switch & headlights are out on both, then a bad headlight switch or headlight switch plug or high/low beam switch plug not fully engaged.
Try applying parking brake
blowen fuse or lights check fuse first
by design the DAY-TIME-RUNNING lights are not intended to be turned off by choice. When you start the 99 blazer with the parking brake on, the DTR lights are off. When you release the parking brake they come on. When you park again and apply the parking brake the DTR lights will stay on, unless you stop the engine and re-start the engine. Since the DTR lights are inter-wired to the regular headlights, they can not be defeated without affecting the regular headlights.
You can only turn off the headlights by applying the emergency brake. When the emergency brake is on, the headlights will not light. Otherwise the best of my expererience is that they are on all the time. If you have remote start, put the emergency brake on before you leave the vehicle and when you remote start it, the headlights will not be on, but the driving lights (if switch is on) will be on as well as the parking lights.
In this order only. Turn engine off. Depress parking brake. Turn engine on. Lights will turn off. To turn lights back on relase parking brake.
Check fuse # 3 , that is a 15 amp fuse for your parking lights if all 4 don't work