MBF1956KEW3 Maytag Refrigerator - Overview

Interior surface of ice tray felt rough & flaky (coating deteriorated) so cubes would not release.
Unplug appliance.
Remove timer cover by hand pressure @ edge.
Remove single attachment screw & bracket at lower front of icemaker.
Disconnect wiring harness from socket @ rear of compartment.
Tricky part was determining what type of connection held the other two attachment points along the long edge of the icemaker. I did not have repair manual or useful drawing but looked @ PartsDirect pic of side brackets & used a small mirror to confirm that mine were also some sort of "snap in" attachment.
Remove icemaker unit by pushing upward and outward on the unit. I takes a good bit of pressure and will pop loose, but be careful not to break attachment bracket from freezer wall.
Scavenge shut off bar and wiring harness from old icemaker once you have it out & attach to new one before installing it back in freezer.
Again, you might find a mirror useful to align those pesky snap-in brackets with the new unit.
Since you probably kept your freezer running while waiting for the part, the plastic snap-ins will be cold and brittle. I warmed them up first by applying a dampened cloth heated in the microwave to make them a little more pliable.
A good push of the new unit towards the snap-ins along with some upward force will get it stable.
Reattach the metal screw in bracket & connect the wiring harness to rear plug... and don't forget to plug the whole thing back in.
It will take awhile for the first batch of cubes dump as the timer may need to cycle completely around to get to the fill cycle... be patient.
Dump the first couple of batches of cubes just to make sure you're free of any residue.

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Having seen this problem before in other equipment so I had an idea where to look. Problem: the automatic defrost function was not operating. Looking through openings in the back panel of the freezer compartment, you could see the evaporator coils and fins were a solid chuck of ice. There are three logical components to check. Heater element, thermostat (located just above the evaporator) and a relay on the control board (located in the fridge control panel). Checked the heater with an ohm meter -- OK. The thermostat closes the circuit at around 20 degrees and opens at around 32 degrees. Pulled out the thermostat, wiring, fan unit. Everything unplugs, unscrews, and unclips, don't cut wires. Put the whole assembly in a friends freezer for an hour or so to see if the thermostat closes -- OK. Problem had to be with the control board. Replaced control board, reprogrammed it per included instruction. Everything is working again.