Your car ran out of coolant and then stopped working as a result. Permanent engine damage has occurred.
If the scenario was that somebody noticed you're coolant was low/out and no symptoms were present, I would entertain the idea that your engine may be fine. However, due to the fact that your engine is now symptomatic after running with no coolant for an undetermined amount of time, it is evident that permanent engine damage has occurred resulting in catastrophic damage. Without taking the engine apart it will be difficult to determine the exact mode of failure in your case. However, what has likely happened is that the metal has fatigued, and warped to such an extent that the tolerances in the engine can no longer support compression.
If you still unsure that your engine isn't just a boat anchor, try getting a compression test done. This will be solid evidence if the engine is sustainable. All a engine needs to run is fuel, compression, and spark. Overheating only endangers compression.
Overheating causes the metal to warp, which would make your engine broken.
Cooling after overheating causes the tension, causing metal to crack.
putting cold water in an overheated engine while it is still hot is a sure-fire way to crack an engine block.
Other common ways to crack an engine block is putting water only in an engine when it's freezing outside (That's why you should use diluted antifreeze in the winter)
Warped engine blocks fail to hold compression for a number of reasons. Most commonly:
- Failing piston rings
- Heads not sealing against the head gasket
- valves fail