starting problem

A "shredding" fan belt that is still attached and being driving the alternator isn't going to be the non starting problem if the engine actually cranks over. If the engine cranks over at least the alternator is charging the battery sufficiently to supply power to the starter. If the engine cranks over the battery and starter must be OK. The engine needs three things to start, fuel (gasoline), ignition (spark) and mechanical integrity (it must develop compression in each cylinder to start ie mechanical components must be in synchronization with each other. If it had run well previous to this no start condition chances are the engine is well mechanically. Had the Check Engine light been on? The engine may have lost spark or fuel which could be due to any one of a number of sensors having failed or the fuel pump or related components are not delivering fuel to the fuel injectors. The engine uses many sensors to report engine temperature, air flow into the engine, crankshaft and crank shaft position sensors to allow the computer in your car to make calculations controlling fuel and spark to the cylinders. It is hard to speculate without being able to hear the engine crank over and do some preliminary tests to determine the cause of your no start condition.

Is your security lights flasing?

My car has done this in the past. Once it was the electronic ignition module which cost about 150 dollars at autozone. The other time it was the crank sensor which a garage replaced for me. It happened to me two times since then and I simply unplugged the crank sensor (which is located under the air conditioning compressor)blew on it and plugged it back in and the car to my surprise started right up. Hope you get lucky and this works for you.