The A320 has 3 hydraulic systems, Yellow circuit, Green circuit and Blue. Yellow and Green systems are pressurised in normal use by the engine driven pumps (that are bolted to the accessory gearbox of each engine). If these pumps fail, the circuit does have electric motor driven pumps that while not being able to produce a flow rate as high as the engine driven ones, produce enough pressure and flow to operate controls as quickly as if fluid was supplied by the EDP. Flap/slat and undercarriage opperation rates would be reduced due to reduced flow rate, but that would be the only a few seconds at most. One system can drive generate pressure and flow into the other (and vice versa) by your noisy PTU. If both the Green and Yellow systems fail, There is always the Blue system that operates all control surfaces via seperate servo actuators to the flying controls and if that circuits electrical pump fails, there is still the Ram Air Turbine (RAT) hydraulic pump avaiable to pressurise it. If all electrics fail, the flight crew still have some control available via mechanical link to the horizionatal stab actuator (THSA) and the Rudder.. Some old Fly by Wire, but not really one that should be wished to be used by any crew..
BTW you have more chance of dying walking out of your house (being in Mexico) than you did in this aircraft incident (that it is, because some system failed when it should not have..)