After my toilet suddenly failed to flush, I took this picture 1.
1.1. Water was dripping from the black Fill Valve with a Column Float.
1.2. There was no water in the white Refill Tube!
Then I closed and opened the water supply Shutoff Valve, which AT FIRST BLUSH APPEARED to fix the hitch! See picture 2.
2.1. No water dripped from the Fill Valve.
2.2. Ta-da! Water was gushing through the Refill Tube!
But alas, when I flushed the toilet next time, the hitch at picture 1 relapsed. Again, I had to close and open the Shutoff Valve to respawn at picture 2. Why?!?!
My toilet looks like, but differs from, this. The differences are the position and kind of Overflow Tube. Mine is covered (the other is UNcovered), and positioned to the upper right (the other is upper left) of the Dual Flush Valve.