I have had a few call backs for this problem.
Usually it is a supply tube with a built in "Flood check" but this is usually for new installations.
Another problem is there is a float and ball on the fill valve, if you look at the fill valve on the side is a square box and at the bottom of that box is a white ball. Sometime that ball gets blocked and the water does not drain from the float keeping the float closed.
The only way to fix this is to replace the fill valve.