Pull your ice bin out and look at the opening where the brass colored rod enters. There is a solenoid (AP3132895) inside the housing that should actuate to move the bucket arm in order to dispense cubes. Stick your finger in there and see if you can get it to drop down. The solenoid may be damaged, or just frozen in place. Once it drops down and with the freezer door open, actuate the door switch with your finger, while pressing the ice lever in the dispenser. Make sure you have selected cube and crushed first. The solenoid if it is working will snap up then fall back down when you release the lever. If it doesn't, then you will need to remove the housing it is in and see if it is full of frost. The solenoid shaft must move freely in order to work properly. They will rust with time and become pitted preventing proper operation.

Are you actuating the door switch when you press the lever? The dispenser only works when the door is closed so you need to block the switch to get it to work.