Ice maker not working. water supply goood. makes loud noise on and off . Maytag Ref. model MZD2665HEB

You need an engineer. That sounds like a 'Clixxon', a device that cycles the compressor on and off due to overheated gasses in the system.

Do you have cats or dogs? Is the condenser coils in the bottom of the unit clean?

This page covers 'clicking sounds'.

https://www.google.com/search?q=maytag+fridge+making+clicking+noise

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hello sir

if ur ice maker

Makes no ice

• Check the shutoff arm
• Check the supply valve
• Inspect the water supply line
• Test the shutoff switch
• Check the freezer temperature
• Inspect the ejector gear
• Test the ejector motor
• Test the ice mold heater
• Test the holding switch
• Test the water inlet switch
• Test the thermostat
• Test the water inlet valve

Turn ice maker off for 12 hr's. Next time you buy a ref. pay the extra $150 for a 5 yr. warrenty. Ice makers break all the time. All of them!

If the water flowed normally for a few years and now will not fill the ice maker with enough water to make full size cubes or dispenser fill too slow the problem may be a defective=> 67005154 Water Inlet Valve In the tutorial above I want you to listen carefully of all the possible items that can cause slow waterflow. I am here should you have questions Thanks Sea Breeze

your water valve is stuck open and needs to be changed

If you need further help, I’m available over the phone at https://www.6ya.com/expert/jason_4570d45317834dd3

The water inlet valve on the back of unit opens when the ice maker needs water. If the valve doesn't seal good because of sediment or wear it will continue to drip and when the water reaches the ice maker supply tube it will freeze blocking the fill tube.. You can take the water line off the valve and watch to see if it drips.

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

Possibly a bad valve but more likely not enough water coming to the unit,follow the water line from the back of the unit to where it hooks to the pipes there is usually a little saddle valve there,try closing it all the way and then open it back up check the water through the door and see if the pressure doesn't improve. 
 You can also remove the Ice maker clear out the fill tube and sit a cup under the end of it for a day or two if you get water in the cup and Ice in the tube you probably have a solenoid valve that isn't closing completely.

im sorry to tell you, but the sound is probobly normal.
fridges these days make some weird noises.
they started making noises when they changed the gas to R34a.
you may be able to get a noise ruduction kit for your model. they are not too fun to install

make sure the wire rod on the ice maker is in the down position in order for it to make and release the ice