The ice maker stopped working on my Kenmore Mod 106.55532400

Is the cold water dispenser working? If not, does the filter need to be changed? Do you actually have water supply to the fridge?
Is the Ice bin empty? Is this your fridge, or are you renting and this was in place? If yours, do you have an Owner's manual with the troubleshooting tips? No manual, try manualslib.com Make model possibly year and serial number. If not yours, there should be a switch that turns the Icemaker on or off. A green light on the front of the drive mechanism near this switch should mean it does have power. No light, no power. There should be a mechanical switch that stops the Ice maker. If the bin is empty, the ice detection arm should be down If it is not down, It is stuck in the "bin is full" position. If these are not the problem, It may be the electrical valve for the Icemaker water supply is not operating, or has been disconnected, or is bad. I have found that one of the online "appliance parts store or sites" have been quite helpful in diagnosing problems and recommending parts and how to fix.

Assuming you followed the water line installation directions and you have water available to your new refrigerator/freezer here is the rest of the "priming" info you requested. (basically it tells you how to run a bunch of water through the system by filling cups or glasses to remove any debris and/or air...

Automatic Ice & Water Dispenser
Priming the Water Supply System
1. Begin filling the tank by pressing and holding a drinking glass against the water dispenser paddle. 2. Keep the glass in this position until water comes out of the dispenser. It may take about 1½ minutes. 3. Continue dispensing water for about three minutes to flush the system and plumbing connections of any impurities (stopping to empty the glass as necessary).
Ice Maker Operation & Care After the refrigerator is installed properly and has cooled for several hours, the ice maker can produce ice within 24 hours. The ice maker will fill the ice bin from the rear. You must dispense some ice to force the ice forward in the bin. This will allow the bin to fill completely.
Turning the Fresh Food Ice Maker On and Off Ice production is controlled by the ice maker's On/Off icon on the control panel. Press and hold the "Ice Off" icon for three seconds to turn the ice maker "ON" or "OFF". The ice maker is turned off when the LED above the "Ice Off" icon is illuminated.
Using the Ice Maker after Installation Before making ice for the first time, be sure to prime the water supply system. Air in new plumbing lines can result in two or three empty ice maker cycles. Furthermore, if the system is not flushed, the first ice cubes may be discolored or have an odd flavor.
CAUTION
For proper dispenser operation, recommended water supply pressure should fall between 30 psi and 100 psi. Excessive pressure may cause water filter to malfunction.
NOTE The water dispenser has a built-in device that shuts off the water flow after three minutes of continuous use. To reset this shutoff device, simply release the dispenser paddle.
IMPORTANT On occasion, unusually small ice cubes may be noticed in the bucket or in dispensed ice. This could occur in normal operation of the ice maker. If you start seeing these more frequently, it may be an indication of low water pressure or the water filter needs to be replaced. As the water filter nears the end of its useful life and becomes clogged with particles, less water is delivered to the ice maker during each cycle. Remember, if it's been six months or longer since you last changed your water filter, replace the water filter with a new one. Poor quality household water may require the filter to be changed more frequently.
IMPORTANT Your ice maker is turned on at the factory so it can work as soon as you install your refrigerator. If you cannot connect a water supply, set the ice maker's On/Off icon to Off and turn off the water supply valve; otherwise, the ice maker's fill valve may make a loud chattering noise when it attempts to operate without water.
Hope this helps. Randy

Refrigerator - Icemaker Not Dispensing,or Not Making Ice Check that the feeler arm on the icemaker is in the down position and is not blocked. If the icemaker does not have a feeler arm make sure the icemaker paddle is not blocked under the icemaker. For more information on the causes of new icemakers not making ice. For more information on normal ice production. Side by Side models: The filter may be loaded with sediment that can cause low water pressure. The water pressure must be between 40 and 120 psi. Pressures below 40 psi may cause a malfunction of the icemaker (i.e. producing hollow cubes or no ice production). Test the water pressure: Dispense water from the dispenser into a large measuring cup for 20 seconds. If the measuring cup contains less than 13.5 ounces (400 metric centimeters), the water flow is inadequate. If the amount of water is less than 13.5 ounces then the refrigerator fails the test, remove the filter and test the refrigerator again with the by-pass plug in place. If the refrigerator dispenses the proper amount of water with the by-pass plug in place, then the filter should be replaced. If you no longer have the by-pass plug and it has been over three months since the filter has been replaced, you should replace the filter. If the refrigerator fails the test again and you know you have the proper water pressure in your home, you should call service to check the refrigerator. If the amount of water collected is over 13.5 ounces then the refrigerator passes the test and the dispenser is working correctly. Ice not Dispensing Due To Clumping Ice: Your dispenser may not be dispensing due to clumping ice cubes. The ice cubes in your icemaker may be clumping for a couple of reasons: Low food load: The defrost cycle radiates heat into the freezer. The ice in the freezer will naturally absorb the heat. This will cause the ice to melt slightly during defrost, then eventually freeze together in clumps. Increasing the food load in the freezer will buffer the warmth from the defrost cycle and keeps the ice from melting. Lack of use: When the ice bin is full, the pressure from the weight of the cubes can cause the bottom cubes to fuse and clump. To prevent this from happening, discard the clumped ice and check the bin periodically to ensure the ice is not building up. If you do not use a large amount of ice, move the feeler arm on the icemaker to the up position to turn off the icemaker and stop ice production. For more information on the causes of clumping cubes. If the ice bucket is not seated correctly, ice will not dispense properly. Make sure the ice bucket is in the correct position. Refer to Use & Care manual.

The ice maker valve is a dual one. with 2 solenoids. One solenoid operates the water and the other the ice maker. So if the water works that don't mean the ice maker supply is ok. The ice maker itself controls the flow of water. So if the water valve is ok then the ice maker is faulty. I have repair photos HERE

If you need further help, reach me via phone at https://www.6ya.com/expert/dan_73bbd84fe1d95b61

If water is also not com out of dispenser then filter should be changed. If water dispenses but ice ice is not being made, the sensor arm or infrared sensor may be stuck or blocked. If sensor is OK then ice maker needs service.

check to see if the hose going into icemaker is frozen. unclog it

make sure you push the ice lever back down

Check the following:

Is the freezer door closed completely?

Is the ice storage bin installed correctly?

Is there ice in the storage bin?

Has the ice frozen in the storage bin?

Is ice stuck in the delivery chute?

Has the wrong ice been added to the storage bin? Use only
cubes produced by the current ice maker.

Has the ice melted around the auger (metal spiral) in the
ice bucket? Dump the ice cubes and clean the ice storage
bin.

Is the ice dispenser stalling while dispensing “crushed”
ice? Change the ice button from “crushed” to “cubed.” If
cubed ice dispenses correctly, depress the button for
“crushed” ice and begin dispensing again.

Has the dispenser arm been held in too long? Ice will stop
dispensing when the arm is held in too long. Wait 3 minutes
for dispenser motor to reset before using again.

The ON/OFF switch is located on the top right side of the freezer
compartment.
To turn the ice maker on, slide the control to the ON (left) position.
To manually turn the ice maker off, slide the control to the OFF
(right) position.
NOTE: Your ice maker has an automatic shutoff. The ice maker
sensors will automatically stop ice production, but the control will
remain in the ON (left) position

REMEMBER:

Allow 24 hours to produce the first batch of ice. Discard the
first three batches of ice produced.

The quality of your ice will be only as good as the quality of the
water supplied to your ice maker. Avoid connecting the ice
maker to a softened water supply. Water softener chemicals
(such as salt) can damage parts of the ice maker and lead to
poor quality ice. If a softened water supply cannot be avoided,
make sure the water softener is operating properly and is well
maintained

The Dispenser Lock (on some models)
Your dispenser can be turned off for easy cleaning or to prevent
unintentional dispensing by small children and pets.
NOTE: The lock feature does not shut off power to the product, to
the ice maker, or to the dispenser light. It simply deactivates the
dispenser levers. The ice and water dispensers will not work.
Style 1: Press the LOCK BUTTON to lock the dispenser. Press the
UNLOCK button to unlock the dispenser.
Style 2: Press and hold the LOCK OUT button to lock the
dispenser. Press and hold the LOCK OUT button a second time to
unlock the dispenser.

http://www.ajmadison.com/ajmadison/itemdocs/2261717.pdf

My icemaker stopped producing ice. We turned off the water line to it when we went on vacation for a week. We turned the water back on when we got home and since that time it won't produce ice. We can still get water from the door dispenser though.

If the pieces of plastic are smaller than the inner diameter of the water tube then you should be looking at the filter washers on the tap and where the water line fits onto the valve assembly behind the fridge. If the filters are clear, the problem is within the ice dispenser. Remove the ice bin and inspect the shroud where the motor coupling pushes onto the auger behind the bin. The auger could be off centre and chaffing the plastic away. Otherwise, check the ice maker fingers for damage.