The first thing to check on an icemaker not getting water (besides making sure it is turned on) is the fill tube that goes through the rear of the cabinet. They can sometimes get frozen shut in which case you may be able to melt any blockage with a hair dryer, etc.
Next the water fill valve should be checked. While both the water dispenser and I/M both use the same water valve, each use a different side of it which work independently of each other. You can read how appliance water fill valves work at the following link: