It sure sounds like the flapper is bad.
What does the flapper look like? Is it the black plug attached to the chain that allows water to exit?
Yes this would be the flapper.
This holds the water in the tank until you push the handle down to flush. It may not be seating right, or it just could be worn out.
I checked it and it is sealed tightly. No water is leaving the tank. It just keeps filling and then runs over in the little tube in the center
So the water does not stop flowing into the tank at all?
No, it just runs for a few seconds and stops and overflows into the center tube. Even if there is vibration on the floor etc. it will cut on and run and stop and flow into the tube.
Would you happen to know what brand of fill valve is in the toilet. This would be the part with the float on it
Is it white , black or gray?
or a lite brown?
No it is just yellow and the toilet is American Standard brand
Ok if the water turns off and then it runs into the overflow then turn back on for short time , and if you have tried to adjust the adjustment screw on the top of the fill valve and this did not work. Then the fill valve is bad or there is debris in the valve, either way I would just replace the fill valve.
I also notice that when it is filling, water comes from outside the yellow cap where I am guessing contains the fill valve. Is this possibly a sure sign that it is bad?
This is part of the fill valve , and this would be a sure sign the valve is bad. I use fluildmaster replacement fill valve, models 400 or pro 45
Most home improvement store and some hardware stores carry this valve.
OK Thanks Todd, you have been a great help, But one last question, The flapper and the seal look great but at the bottom where this assembly is attached to the tank, the black seal around that is chipping after I was messing with it. Should this be replaced or leave alone, I don't see any leaks, just tiny black particles in the tank
Yes I would replace the flapper also they run about $5, this way you covered all the bases
I may have miss understood you on the last question . Are you talking about the rubber gasket on the bottom of the white tube?
Or the black seal on the bottom of the fill valve.
Where it goes through the tank.
I am talking about the rubber seal beneath the flapper directly on the bottom of the tank
If there is nothing leaking under the tank (between the tank and bowl) I would not mess with this. This seal is very large and there should be plenty of rubber left to seal this flush valve
the Flush valve in what the flapper hooks to
Thanks Todd You have been a great help.