Like stated in the summary, my toilet tank won't fill up unless I turn off the water valve (beneath the tank) and then turn it back on again. I don't have the ballcock type assembly. I have the 400A type of fill valve.

Let me add that right before this started happening, I turned off the main water supply to the house, turned on all the faucets and flushed the toilet until water stopped running from the faucets and toilet. Then I turned off all the faucets and slowly turned back on the main water supply. (I did that because another site said that that would fix knocking pipes.) Anyway, the next time the toilet was used (about 1/2 hour later), the tank did not fill. But if I turn off the water valve under the tank and then turn it back on, the toilet will fill. But I have to do that every time the toilet is flushed.