Depending on the fill valve, the float may be rubbing on something, and not dropping to open the valve, or it could be internal to the valve. Take the cover off the tank and watch to see what's going on. As mentioned, it could also be the supply valve or the hose connecting the shutoff to the fill valve.
One simple test is to first turn off the water, then remove the hose from the fill valve, then after pointing it into either the toilet or a bucket, turn the valve back on. If you get water out, it's probably in the toilet, if not, it's the valve.