The car won't start because the pulley that powers the water pump came off.
If you are talking about the pulley directly below the water pump, that is the crankshaft pulley, also called the harmonic balancer. The pulley for the belt bolts to the balancer. If the entire assembly came off that would cause the car not to start. The crankshaft position sensor reads the speed of that pulley to time the ignition and fuel delivery. I've never seen that happen before. It's possible the crankshaft broke as well. A qualified mechanic, such as one from YourMechanic, would be happy to inspect your car's no-start problem and provide an estimate or recommendation to get your car running again. If your car needs its harmonic balancer replaced, the mechanic will be able to complete this job for you as well.
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