The ice cubes from our automatic icemaker freeze into a solid block within 24 hours. The icemaker seems to be working fine, the cubes are all coming out. The refrigerator is working great. The freezer seems ok except for this problem. We have a Kenmore, top mount freezer that is 4 years old.

You need to replace the water valve

Good day,
Either the water valve opens to fill the ice maker cavity, and doesn't shut off soon enough, causing the ice maker to overflow.
Normal file time is approx. 7 seconds.
This is the most common problem.
As well, it is possible the micro switch in the ice-maker that tells the valve to open and close has malfunctioned.
This is all based on the fact that the freezer maintains a normal temperature.
To test the freezer for consistency, place a plastic glass in the freezer half full of water.
Check it in 8 hours. It should be frozen solid. Then place the glass in a plastic bowl, and lay the glass on it's side. Recheck in 24 hours. The ice should remain in the glass.
If not, there is a problem with the refrigeration system.

The icemaker produces small cubes if the water fed into it is not enough and lumped together if too much water is supplied. In order to obtain the desired size of ice cubes, the amount of water supplied to the ice maker needs to be adjusted. Adjust the valve supplying water to the icemaker or the unit in general in such a way that right amount of water fills the ice tray.

HAVE A LEAK COMING FROM SOMEWHERE CAUSING ICE TO FREEZE TOGETHER TUBE WHERE WATER COMES IN MAYBE PARTIALLY FROZEN

majority of refrigerators today are equipped with an automatic icemaker. The water valve supplying the icemaker is a key component of the icemaking system, and it should be the first thing you check if the icemaker's performance is erratic or if the icemaker stops working. When the icemaker calls for ice, its switch closes an electrical circuit and energizes the solenoid-operated water valve. This allows water to flow through the valve and into the ice cube tray. The water is frozen into cubes, and the cubes are dumped into the ice bin. As time passes, strange things may happen to the refrigerator's icemaking capability. The cubes may be small or there may be a solid chunk of ice instead of individual cubes. It's also possible that the icemaker will stop working. These are all signs of a malfunctioning water valve. The valve is equipped with a screen on its inlet to remove minerals and sediments in the water supply. Over time, minerals and sediment build up on the screen and restrict flow through the valve, or even block it completely. Minerals that make it through the screen can cause the valve to stick in the open position, overfilling the ice cube tray in the process. This is a common problem in areas with hard water, but it can happen just about anywhere. Another malfunction that will cause the icemaker to stop working is a break in the solenoid coil winding. This is known as an open coil. The coil winding generates a magnetic field as current passes through it, and this magnetic field opens the plunger valve that controls water flow. A break in the coil winding stops current flow and this prevents the valve from operating. Test And Inspect The icemaker's valve is easy to inspect and test. First, gently pull the refrigerator away from the wall, and unplug it. Turn off the water supply to the icemaker by closing the shut-off valve in the copper waterline leading to the valve (Fig. 1). Use a screwdriver or nutdriver to remove the rear lower access panel from the refrigerator's back. Next, remove the fill tubing from the water valve. Use a wrench to loosen the flare nut on the brass fitting on the inlet side of the valve (above). Place a container under the valve to catch the small amount of water that will spill from the valve and tubing. Now use a screwdriver or a nutdriver to remove the screw holding the valve's mounting bracket to the refrigerator cabinet (Fig. 2). Pull the valve out of the compartment and remove the tube on the valve's outlet. Then, remove the solenoid's electrical contacts (Fig. 3).

replace water valve

Depends on the model. It could be a water switch that is sticking or a motor in the icemaker running to slow. My advise is to replace the faceplate of the icemaker. Part #150

icemaker have problem

Try using an hairdryer or defrosting the unit completely , this often get rid of blockage caused by frozen lines fixing the problem.

The water lines can also be unblocked from dirt using a thin flexible shaft. This after defrosting.

If all that does not fix the problem, then you may need to replace the water valve, the icemaker solenoid, or the whole icemaker assembly.

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Appliance Parts Pros

•  if the cubes that the icemaker makes are full size then... the water valve on the back of the machine is usually the culprit in these cases. it will not close fast enough resulting in a little overflow of water into the auger assembly every time it makes ice. it only takes a little bit of water to settle in the bottom of the pan to cause problems. 
  
• if the cubes are smaller than what you would expect then the water is leaking out right before it reaches the icemaker. either from the plastic tube behind the icemaker or the cup on the icemaker that funnels the water into the icemaker.
• it also could be the timer inside the icemaker leaving the water valve on too long.
• all these things can be tested on site. the service person must not be very well trained.

if you already checked this and think it is a different problem then let me know, i will help you figure it out. 
Mike