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is this an earlier shape Galaxy (2000 to 2006)?
you need to be looking at the wiring to the doors especially the front doors. Where the wiring goes between the car body and the door it runs inside a rubber tube, with opening and shutting the doors eventually the wiring becomes damaged inside the tube and can either become broken or shorts together,this is why the windows are affected as they get their power and earth through this wiring.
The indicators start to work because they are linked to the locking of the car,when you lock the car they flash once when you unlock the car they flash twice,if due to a short circuit in the door wiring the lock/unlock signal is sent to the locking control unit then this unit sends power to the indicators because it thinks the car is being locked or unlocked via the lock in the doors.