First, make sure that your opponent has their target unit currently on and that it has fresh batteries. If the unit isn’t making noise when hit, then your opponent’s unit has already been hit 10 times and is currently in Shut Down mode. Have them turn their Target Unit off and then on again to reset it (make sure to reset your own target unit as well when starting a new game).
Your gun is currently out of shots and needs to be reloaded. Press the Arm button under your blaster’s barrel to reload it, and you’ll have 25 shots to fire. If your gun still isn’t making any sounds when you pull the trigger to indicate that it’s firing, then the batteries are likely out. Insert 3 new “AAA” batteries into your blaster’s Target unit and it should then work correctly.