Our Kenmore ref had been not cooling for a week, I tried to reset it, but it's not cooling and no ice, the motor sounds working and the lights are on when opened

Sounds like cooling coils inside ref. that cools the water before the dispenser in the door.
These coils are in the back bottom of ref, behind crispers. They may be leaking.
Here is some more help.

I'm including my article on Refrigerator Repair for your help and convenience.;
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http://www.fixya.com/support/r5816737-fix_refrigerator_psychologically

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MORE TIPS AND TRICKS:
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WATER SPLASHING IN FREEZER AT ICEMAKER
THE FILL TUBE IN BACK OF REFRIGERATOR CAN SLIP
AGAINST THE FILL RESERVOIR CAUSING A PARTIAL BLOCKAGE
OR BECOME CLOGGED WITH ICE.
REMOVE THE ICEMAKER AND INSPECT THE FILL TUBE.
RUN WATER IN TUBE TO ELININATE BLOCKAGE AND CHECK
TEMP IN FREEZER. IF TEMP IS BELOW 0 DEGREES, THATS
OVERKILL AND USUALLY A WASTE OF ELECTRICITY TO KEEP IT THAT COLD, NOT TO MENTION THE FILL TUBE FREEZING UP
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Leo Ponder
imufo2
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in the past i have seen this happen when the ice ben is emoved and the drive impeller is not seated properly usually due to ice ect. Its a pain but take out the ben and see if the motor turns normally. you can hold the door switch closed by hand and have someone push the button for ice if the motor turns you have the problem i have said. If not your door switch is bad and needs to be replaced it controlls the power to the bulb and the ice maker motor. You can pop the door switch out with a flatblade screw driver but have a replacement on hand wire plug into the back of it the switch is an on off switch. Make sure you unplug the ref first electricity bites...

how old is your kenmore? it sounds like the Ice maker thermostat is broke it happened on mine

Make sure that the bucket is pushed in all the way. If the motor is running the screw should be turning. I would also take the bucket out and try to turn the auger by hand to make sure it is turning free.
Please rate solution if helpful. Thanks

1. Get the Food out of the Ref and Freezer. Unplug the power cord from the wall.
2. The cooling coil is in the back wall of the freezer side. Working from inside the Freezer.
3. Remove the back plastic cover to expose the cooling coil. It's called the Evaporator coil.
4. Use a hair dryer to melt all ice off the coil.
5. Put it back together. It should work for 3 - 5 days now at least.
6. Put a thermometer in there. After 24 hrs. the freezer should be 0 to 10 degrees F. and the Ref. side 37 to 44 degree F.
7. Check the door gaskets for tight fit, using a dollar bill for a gauge.
Shut the door on the dollar and try to pull it out in several places.

If it ices up again in a week or two, you have a defrost heater problem. There is a electric heat strip around the cooling coil. This heat strip comes on about 10 minutes every 8 or 10 hours. This heater melts the ice off the coil. There is a clock timer device under the ref. that cycles the heat strip. You may have a bad clock, fuse device or burned out defrost heater strip. The cooling coil must be ice free to work properly.

IS this unit a frost free? I'm wondering if the motor in your timer is running slow.If that happens it could take too long before the freeze cycle comes back on. Or check the terminator out. Either that or check the electric to make sure nothing shuts off the unit like a timer for the lights.

its the problem of the motor which runs the fan.that motor needs replacement.a very chance it can be possible that the motor is perfect but the wirings from the motor which connects to the fan are faulty and got cut in between.but it can be possible.so first check out the wirings if they r perfect then its faulty fan  motor.get it replaced. thanks.

The fan behind the molding is hitting some ice build up and causing the sound. Sounds like the timer for the defrost isn't working. Try to turn off the unit for few hours or take off the molding in the freezer compartment and remove the ice build up with hair dryer.

I have a kenmore coldspot side by side model # 106.53662300.
The ice maker red light is blinking and it has made very little ice in the last 24 hours. What do you think the problem is?

check the rear of the freezer you may find a build up of ice there if so you have a defrost problem chances are the heater is bad you can unplug ref and let thaw or you can tear into the rear (pretty easy) and defrost with hair dryer and look at theheater which is a glass tube usual only one at the bottom of the coils but some models have two one in the center you will most likely find them bad if they are not chrome looking then they are bad replace defrost thermostat also this is common rule.let me know what you find god luck