With the valve turned off, disconnect the pipe from the bottom of the toilet (normally you don't need anything except your hand to do this, expecially if it is new unless they used a solid riser pipe); have a bucket handy, then turn the valve back on and see if there is anything coming out. That will tell you if the problem is in the refill valve in the toilet (it could be clogged or sticking), or the shutoff valve itself. If you don't get any water out of the (probably a flexible hose you took off of the toilet), then shut the valve off again, and take the other end of the hose off. Then, carefully, since it will now be a fountain if it works, turn it back on. If you still don't have any water, then the valve is stuck or clogged. Depending on the type of valve, they are pretty inexpensive. Instead of trying to repair it, replace it (maybe $5 at HD). It is probably a compression valve - see if the part next to the wall has a nut on it. If so, then you can shut off the main water, loosen that nut until it is free of the valve, slide the valve off, then replace it with the new one (you can reuse the existing nut and sleeve that will probably stick on the pipe).
If that doesn't do it, and you have water coming out of the hose in the first step, then the toilet refill valve is stuck or clogged. Cleaning that out depends on the brand. Most of them are easy to do, but you need to know the brand. Since it was continually running (did I get that right?), the valve probably has some crud in the seal, which if it is cleaned out, will restore it. The refill valve in the toilet is pretty cheap to replace, too, but that's another story. Fluidmaster valves work for most toilets, and are less than $10. My unprofessional opinion.