So, you’re saying that if you shut off the water to the toilet and then turn it back on, the toilet will refill? Assuming it’s a multi-turn valve, the screw on the bottom of the stem probably backed itself off and the washer is moving around freely. Closing and reopening the valve gets it out of the way.
If you’re feeling adventurous, shut off the house water, remove the stem and see what’s going on. But I wouldn’t do it with A)a new valve ready to go in case this one can’t be put back together and B)it’s during Home Depot’s business hours since plumbing projects require multiple trips to the hardware store and you’re not going to be able to turn your house water back on until you get the valve put back together.
But, I would still check the float in the toilet. The pressure drop/increase might be enough to trip a stuck float inside the toilet and my original theory wouldn’t make much sense unless someone’s been using the supply valve recently.
Take the lid off the toilet, flush it, and when it doesn’t refill, make sure the float is dropping with the water. If it isn’t just push it down by hand and it should refill. I would check that before tearing apart the supply valve. (The float will either be a big ball on a metal stem or a collar around the big plastic tube on the left hand side of the tank).