Sounds like the heater circuit in your icemaker is bad so it's not releasing
the cubes properly. It could also have corrosion causing the antistick
surface to flake off - did you have any black plast piece in the ice before?
Buy a new ice maker. There are only a couple of styles used in most
refrigerators so you can likely use the generic models they sell at Home
Depot or Lowes. Find one that looks the same. If the wiring harness is
different just use the plug pigtail from the old one. It's a simple fix and
you can do it in less than 30 minutes.