Model FRS26ZRG when using the cube or crushed ice door dispenser the ice does not come through the flap it just builds up in the door.
It seems to me that when you push your glass against the lever the flap to let the ice come through would open at the same time.
On the dispenser there is a heat motor 218740003 that should allow the dispenser door to open. You will want to check to make sure that this is working. Also you will want to check the arm 5304401778 of the dispenser door to make sure that it is not broken. If it is then it will need to be replaced.