With the burned rubber smell & all, these symptoms starting after an unusually quick start, I’m sort of concerned about the timing belt. The timing belt is stressed more during quick accelerations. Does a 2000 Protege have a rubber timing belt? Does this car have a 1.6L DOHC engine? I think that one does have a timing belt, and the inspection interval is 60k, and 90k, and replacement recommended at 105K. Double check your owner’s manual or w/Mazda dealership as these specs varies car to car & even in the state the car was sold.
In any event, if the timing belt has broken or jammed, that would prevent the engine from starting. If you think that is even a possiblity, don’t attempt to start it again until you’ve towed it to a mechanic and had him verify the timing belt condition, as starting the engine w/a broken timing belt can do serious damage to the valves. Which is something you definitely don’t want.
Edit. The 1.6 from what I see is a free-wheeler, so the fact that you’ve attempted to start it may not mean the valves are toast. Yet. But with these symptoms it is safer to have a mechanic do a look-see before trying to start it again.