OK this is how it works, water is connected at the back to the supply, it then passes through a water inlet valve that is controlled by the water selector at the front, it then passes under the appliance and into the fridge area where it is chilled and then back out of the fridge, under and towards the front where it joins the pipe connecting the door supply pipe. Areas to check are as follows, you will already have checked some but bear with me ~~
a. check that you have main water supply to the screw in connector at the back.
b. check that water is passing through the valve to the pipe that goes to the water chiller in the fridge. You will have to disconnect the pipe behind the cover and have someone active the water from the front whilst you check with a towel that water is coming through the valve.
c/ Check that the chiller coil is not frozen up in the fridge.
e. Check the pipe push fit connector under the appliance has a water supply by disconnecting one end and once again activating the water supply
d. If you check all these out at one point you will find water and the next there will be non, once this situation is found you know where your problem is.
Come back to me once you have done these checks - Ian