They definitely lost system one, evident by the fact the nose gear doors were open but the gear failed to retract, and they show that the wing gear is retracted from the computer generated pictures and overlay of the gear in a down position.
System 1 & 2 hydraulic pressure and return lines are grouped together on the left side passing through the rear pressure bulkhead so it's possible system 2 was lost as well.
If so they would have lost both the left inboard and left outboard elevator leaving them with only 50% elevator control and 1/2 rate stabilizer movement.
It appears from the simulator (not designed or certified for outside CofG) exercise that full nose down elevator and forward trim "may" have allowed them to control the aircraft but that's with full flight controls!