My turrets won't fire at the locked target.

You're probably out of range.

The range indicator above the turret in the module bar turns green when in range. Close in until it does.

If it's green and they still hold fire, check:

1. The lock: pressing Tab on your locked target unlocks it. Press Tab to lock again.
2. Sensors: the target must be inside your sensor range with line of sight. A blip can't be targeted.
3. Heat: during a SCRAM your turret batteries are suspended while heat is held at zero for 3 seconds.
4. Enemy ECM: a Tracking Disruptor briefly disables its target's turrets, and a Signal Jammer briefly stops nearby enemies' turret fire.
5. A Remote Tracking Shroud stops enemy turrets firing on the squadmate it covers.

To reach further: Triangulator (+10% turret range) or Tracking Computer (briefly +100% sensor range).