Foam to fill toilet mating surface gap

It seems as if you have an obstruction that may be floating around in the pipe or valve. Sometimes it obstructs sometimes it flows clear. I would start with changing the water valve. If this is the old style "gate" valve there are several things that can clog the line. I would replace it with a 1/4 turn ball valve. That will give you much better flow than a gate valve. You will need to shut down the water probably at the main. The old valve is probably soldered, but you could cut it off and use a compression type valve instead. "Sharkbite" is one such supplier. Although I have never used their compression valve, I have used their end caps and found them to work well.

If you can have someone hold a bucket under the pipe once you cut off the valve and then a second person turns on the water main to fill the bucket to purge the line of any debris. With cast iron pipes it is common to get clogs from rust build up. The rust may not pass the small opening in the old gate valve when you first purged the line.. Although you did not mention what type of pipes you have, if it's copper than you won't normally find rust obstructions..

Get something like this http://www.amazon.com/dp/B00KHSLV2G or this http://www.amazon.com/dp/B000BQUJEA (there are other types, those just came up first when I searched).

In case the links break: They are wax ring alternatives that are made of flexible plastic instead of wax, so they can take some movement without leaking. There are a bunch of different types with lots of different designs. I have never used them so I can't recommend any particular one.