After you hit the rock, did you tilt the mower on its side to look under it?
If you did, this let some oil go from the breather to the carburetor. Look at the air filter. Is it oil soaked?
When you tried to start it, it sucked some of this oil into the engine and blew it out the exhaust.
If it didn't shear the flywheel key, and depending on how much oil ended up in the carb and cylinder, you might get it started.
If it wont run, you may have sheared a flywheel key, or it could just have too much oil in the cylinder. I've had to clean the oil out of some carbs before they would run. All the oil also might have destroyed the spark plug.
When you do get it started, it will smoke really bad until it gets hot enough to burn all the oil out of the muffler.
If it vibrates after you get it started, you may have a bent blade and/or bent crankshaft.