"IF" you have verified the valve is open and you think there's something stuck you can buy a cap for your outlet connection that also has a hose connection like this one.
Sewer capYou can then connect a garden hose and turn the water on just a bit and see if the water flows back into the tank. If it does you can turn it on a bit more and hopefully get whatever is there out. You will want 2 people so you can push the valve closed at the same time someone is shutting off the water and there will only be minimal mess.
From inside, if you open the toilet flush valve, can you see anything? If you pour a 5 gallon bucket of water down the toilet do you get 5 gallons out pretty quickly or is that where you only get a trickle?