Can I still open my garage with broken springs?

You can still open your garage door with broken springs, but you should not try to open it with the automatic opener. Without the springs counterbalancing the weight, the door is effectively a 150 to 350 pound dead weight, and forcing the opener to lift it will burn out the motor, strip the gears, or pull the opener off its ceiling mount. The safe approach is to pull the red emergency release cord to disconnect the trolley, then have two people manually lift the door together. Once it is open, prop it in place with vice grips clamped onto the tracks under the bottom rollers so it cannot crash down. Then call for spring replacement before using the door again.