Ice cube are not dipensed only crushed ice
Remove the ice bin, and in the back of the freezer you'll see a square opening with a white plastic piece inside. When you dispense cubed ice this piece lifts up, lifting the long metal rod that runs along the bottom of the ice bin. When that rod lifts it opens the ice flap at the front of bin, allowing cubes to be dispensed. If the flap is not open, the cubes will be ground against the cutters and you will get crushed ice.
I had the same problem you do - the solenoid that lifts that white plastic piece is dead. But I also rent the place where I live, and it comes with the fridge. It's not likely the landlord will want to deal with this issue since I can still get ice, not considered a necessity, etc. So here's what I did to make it so that I always get cubed ice.
Take a wine cork and stand it on end. Using a good knife, I positioned the blade about 1/3 of the diameter from the edge and cut all the way through the length of the cork. Then remove the ice tray.
Now put your finger in the sqaure opening and lift up the white pastic piece. Slide the modified cork under the flap so that it is jammed into the raised position. (This is the position it should be in when you are asking for cubed ice.) Now slide the ice tray back in while using your left hand to push the plastic ice flap at the front of the tray to the left side (again, the position it should be in for delivering cubed ice). Peer under the tray while you're slowly sliding it back in so that you can see if the metal rod connected to that ice flap successfully slides into the square opening at the back. If it can't slide in above the cork-raised plastic piece, you may need to pull the cork back out and trim a little more off it.
This worked for me... I can't get crushed ice anymore, but I've only needed crushed ice once in the 16 months I've lived here so that's not an issue for me.