Welcome to Just Answer.
Sorry to hear about your problem.
Sounds like the flapper is not seating correctly, which is allowing water to leave the tank and enter into the bowl; this would cause the fill valve to keep running as it continuously tries to keep the tank full.
You need to look in the tank by taking off the top cover, to see if the chain to the flapper is either caught on something, or more likely the flapper may be old and need to be replaced. The flapper or flapper opening can form deposits that will allow water to leak by, which will cause the water to run. Also an old flapper that has lost it's flexibility will not seal well on the opening and will cause water to pass by. You will need to replace the flapper and this is a very easy job to do.
Watch the short video below to learn more.
Also, verify that the water is not filling the tank too high and going into the overflow pipe and that the refill tube is clipped to the overflow pipe.
If you need further help or clarification on this answer, please do not hesitate to reply to this post.
Thanks for asking your question at Just Answer.
Best of Luck, Brian
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Sorry about that.
This one is actually more informative.
The second video should work, I just tested it.
Let me know.
OK, that video works. The set up in the video is different than mine, but I understand the principle. My house is only 4 years old, before I replaced the entire assembly, I took a towel and wiped around the edge of the valve, hoping to dislodge any buildup. Right now it is working fine. But if it returns, I will replace it.
Very good. Sounds like you know how to handle the problem now.
Thank you for accepting my answer and please leave feedback at your convenience.
Have a great day.