Learn how your appliance is supposed to operate so you can determine if it is malfunctioning.
There is usually a 'sediment screen' in the fridge's water supply line at the the water fill valve on the back of the fridge that can become completely blocked by minerals and debris from the water supply in your house. Move the refrigerator out from the wall and remove the rear access panel. Turn the water off at the wall or tap on the house water pipe and disconnect the supply line from the water valve (it is usually the same size connector as a garden hose). Clean out the screen and reassemble the water line. Check for leaks at the connection and to see if the water comes into the icemaker now.
While you're at the rear of the refrigerator, check the water valve's solenoid coil for continuity. If it is electrically open, the valve is defective and needs to be replaced.
The supply tube that goes through the cabinet to the icemaker can also sometimes freeze closed. That 'fill tube' can sometimes be thawed by squirting hot water from a turkey baster into it. The use of a hair dryer can also sometimes be employed if care is taken not to melt any plastic parts in the area. If this tube repeatedly freezes closed, it may be due to lack of water pressure at the fridge's water valve, possible caused by a partially plugged sediment screen (see above).
All of the information in these Appliance Clinic procedures is provided FREE OF CHARGE. No liability is assumed by the author for the accuracy of the contents or damages caused by the use of these procedures.