Was the water dispenser working fine before you shut the water off?
The reason I am asking this is if it was a water pressure problem then you would have the same thing happening with the water dispenser.
If that is working fine then is likely to be your water in let valve .
The valve is located at the back of the fridge where the water line is hooked.
You should be able to replace it.
Here is a picture of your water valve.  |